Even an HTML5 parser is harder than it looks to implement to the level needed for a browser. You have to build a proper DOM, you have to be secure against all kinds of fuzzing, you have to implement off-main-thread parsing and speculative readahead for performance, you have integrate it correctly the HTML5 event loop for document.write() etc, you have to support innerHTML and so on.
Likewise building a JS engine is impressive, but I do not believe a Web-compatible competitive-performance JS engine can be built by any single person.