I've been, in my mine and on paper, designing a similar house for decades. Only my idea is not nearly so cartoonish, but rather inspired by my love for geology and science.
My place would be more like a modern science museum, with realistic rock formations for walls. It would have several interior water features including a small waterfall, pond, and narrow winding stream with arched walkover bridge. Large plate glass windows with incredible views of genuine (matching) rock formations and other interesting natural scenery.
I would fill it with embedded displays of natural exhibits, such as cool rock specimens, minerals and fossils, and also live animal displays (fish, reptiles, etc). There would be large openings in the ceilings of the synthetic rock interior with great views of the sky for both daytime and nighttime sky observing.
I’ve been, in my mine
in my MIND
Have your ever been to House on the Rock?
Very near your description.