Heat oil in a large heavy-duty roasting pan over high heat. When pan is hot, add onion and cook until crisp-tender, about 1 1/2 minutes. Add ginger; cook until fragrant, about 30 seconds longer. Add snow peas, carrots, and mushrooms and cook, stirring occasionally, until crisp-tender, 3 to 4 minutes. Add edamame; cook to warm through, about a minute longer.