CMU lecture notes [0] I think approach it in an intuitive way, starting from the Gaussian noise linear model, deriving log-likelihood, and presenting the analytic approach. Misses the bridge to gradient methods though.

For gradients, Stanford CS229 [1] jumps right into it.

[0] https://www.stat.cmu.edu/~cshalizi/mreg/15/lectures/06/lectu...

[1] https://cs229.stanford.edu/lectures-spring2022/main_notes.pd...