Heat oil in a 10-inch nonstick skillet over medium heat. Add shallot; cook, stirring, until translucent, 3 to 5 minutes. Add mushroom caps; cook until tender, 8 to 10 minutes.
Add 3/4 cup water and green beans; season with salt and pepper. Stir to combine; reduce heat to low. Cover; cook until beans are crisp-tender, 7 to 10 minutes. If any liquid remains, raise heat, and cook until it evaporates.