Heat oil in a large skillet over medium heat. Add onion and garlic; cook and stir until tender, about 5 minutes. Stir in mushrooms, 1/2 cup water, wine, bouillon cube, basil, salt, and pepper; bring to a boil.

Reduce the heat and simmer, uncovered and stirring occasionally, for 10 minutes. Mix remaining 1/4 cup water and cornstarch together in a small bowl; stir into mushroom mixture and cook until thickened, about 5 minutes.