In a large bowl, toss squash with egg. Place the cornmeal in a large resealable plastic bag. Add squash slices, a few at a time, and shake to coat. Let stand for 10 minutes.
In a large skillet, melt 1/4 cup butter. Add half of the squash. Cook over medium heat until browned on both sides, about 5 minutes. Remove to paper towels to drain. Repeat with remaining squash and 1/4 cup butter; set aside and keep warm.
In another skillet, saute the onion and peppers in remaining butter until tender. Add the hominy, salt and pepper; cook and stir until heated through and golden brown. Stir in the reserved squash. Serve immediately.