Shell peas and add to favas. Meanwhile, in a saucepan, bring a few inches of water to a boil. Add wax beans and cook 2 minutes. Drain, then plunge into ice water. Drain again. Set aside.
Prepare asparagus by breaking tough ends off where they give, and then peel each stalk. Cut trimmed asparagus diagonally into 2-inch lengths. Set aside.
Warm 2 tablespoons olive oil in a large skillet over medium-high heat. Add onion and cook until fragrant, about 2 minutes, stirring frequently. Add garlic and cook another minute or so, stirring frequently.
Add remaining 2 tablespoons olive oil and asparagus, turn heat to medium-low, and cook until asparagus are just tender when pierced with a fork, 5 to 7 minutes depending upon their thickness and freshness. Shake pan to prevent asparagus from sticking.
Add wax beans and stir to incorporate. Add wine or water and gently fold in favas and peas. Season with salt and pepper and cook just until favas and peas are warm, about 1 minute. Adjust seasoning, if necessary, before turning onto a warm serving platter. Scatter with mint chiffonade and drizzle with high-quality extra-virgin olive oil, if desired.