The technology world is shaped like an inverted pyramid, and I suspect that everyone's T is just a small segment of that pyramid. I was fortunate to study computer engineering at a liberal-arts university that tried to build competent engineers by training them with triangular, rather than T-shaped knowledge. The learning curve went something like this:
As the parent pointed out, it's all built on sand - not in the manner they meant, but it's actually built on silicon. At some level, physics and chemistry can teach you about electrons and orbitals and excitation. You can learn about insulators, conductors, and semiconductors. In the lab, you can get some glass plates coated with (clear, conductive) titanium dioxide, an electrolyte, and some Ruthenium or organic dyes, and make a dye-sensitized solar cell, or a tungsten wire and chip of germanium and make a point-contact diode. A little more physics and you can build a bipolar transistor or field-effect transistor.
With that physics as the tip of the pyramid, now branching out with the help of commercial discrete components, you can expand into electrical engineering. On a breadboard, you can make a NOT gate, an AND gate, an SR latch, an SRAM cell. Realize that there's a whole breadth of analog electronics, but we're in a computer engineering course, so consign yourself to a cursory introduction and again climb the pyramid to commercial 7400-series logic ICs, and make a binary adder. Realize that there are lots of 7400-series ICs, with various applications, parameters, and specifications, the pyramid is already staggeringly broad. You know how to move sideways here, but don't right now - climb up and expand further to CPLD and FPGA development boards and some VHDL, rebuild your binary adder in silicon, make a seven-segment decoder, add some load/store instructions, conditional logic, and a few more math primitives; you've got a CPU.
Now that you know how to build a CPU, go buy an Arduino, it contains a small CPU. But don't download the IDE yet, instead, get avrgcc and become familiar with AVR assembly language. Write a main.s, you can blink some LEDs or drive a hobby servo with a PID loop in response to a sensor. There are lots of microcontrollers like PICs, 8051s, and ARMs, and lots of work done in assembly, but we can't linger here - we have to keep climbing the ladder.
Speaking of ARM microcontrollers, grab an ARM dev board. You made a few function calls in your assembly programs, learn about the C ABI. Start learning C on a PC, manipulating text, once you're familiar enough with the syntax to write a "Zork", head back to the dev board and write a Forth, talk to some sensors over SPI, UARTs, and I2C. Write an RTOS, digging through Linux source code to learn about syscalls. OK, your RTOS sucks, and isn't very good at securing real-time constrains when your user code has bugs much less malicious inputs, but it's an OS, here's FreeRTOS. Hook your board to another students' GPIO (optocouplers are handy) and develop a packet network. Install uIP on your boards, and start talking Internet Protocol over sockets. Send an HTML page. Embed some Javascript. Realize that your Cortex-M0 is really resource-constrained, and set up your webpage on a VPS. Install Python on the VPS, and build a web framework. Try to keep track of data in CSV files, redo that as a database, someone already did that and it's called SQLite. And so on up the chain. Down the chain, nothing is a black box, it's all built on sand.
Every level of the pyramid is occupied by someone with T-shaped knowledge. Those just below you are writing the frameworks that you have so much experience in, they're using languages and operating systems that someone with experience closer to the hardware than them developed. Those left and right of you are using different frameworks, with a different path to the electron at the bottom of the pyramid, those above you are your clients who use your products. Further up the pyramid are people who don't know exactly how things get done, they have a lot of things to keep track of, fortunately their vendors (your clients) have software to do that.
The idea that everyone needs to have the base of their T reach the atomic physics at the tip of the pyramid is a little antiquated, even more so the idea that everyone needs to know everything below their framework. That may have been true in the 6502 era, and for a few exceptional people like Carmack or Knuth or Ritchie for some time beyond that. But few can be expected to maintain encyclopedic knowledge of the esoteric alternatives that don't lead up to their T, and no one can keep track of what every user - who may also be a developer - is developing in real time.