i have a similar idea, but a little more complicated where you would then build a tiny house on top of that, only not directly over it, but only half way covering it. extend the top roof of that, and use the other half of the "basement" ish area like a porch/sunroom/greenhouse.
i like the combination of part cave, part underground /earth bermed, and a big cap...with solar/greenhouse and all light that sticks up from an underground house. i like it all smooshed together like that. the cave balances out the solar, with a lot of thermal mass to store that solar.
fi your curious, i made a post with the design in it -->
https://permies.com/t/53140/epic-greenhouse-built-virtually-sketchup
but basic gist is build something similar to what you are describing, ans embed a tiny house over it, but only covering half of it. then have an all encompassing roof the covers all of it much higher up. so this is a tiny house embedded in a greenhouse, basically...with with half the basement are underneath and half on the higher ground. levels .
the other half is open to the greenhouse /porch/ open area.