How to Make It
If using fresh peas, blanch them in a medium saucepan of boiling water until tender but still bright green, about 5 minutes; drain. In a blender, puree half of the blanched or thawed frozen peas with 2 tablespoons of water until smooth. Season the green pea puree with salt and pepper.
Rinse out the saucepan. Add 2 1/2 cups of salted water and bring to a boil. Add the oats and cook over moderately low heat, stirring frequently, until al dente, about 25 minutes. Stir in the pea puree, butter and the remaining whole peas and season with salt and pepper.
Meanwhile, in a medium skillet, heat 1 tablespoon of the olive oil until shimmering. Add the shallot and garlic and cook over moderately high heat until softened, about 1 minute. Add the yellow squash and zucchini and cook over moderate heat, stirring occasionally, just until tender, 6 to 7 minutes. Add the grape tomatoes and cook for 3 minutes, crushing them lightly. Season with salt and pepper and keep warm.
Heat 2 tablespoons of the olive oil in each of 2 large skillets until shimmering. Season the quail with salt and pepper and add 4 to each skillet, breast side down. Cook over moderately high heat until crisp, about 3 minutes. Turn and cook for 1 minute longer. Transfer all the quail to 1 skillet, breast side up, and continue cooking for 2 minutes longer, until cooked through and the skin is very crisp.
Meanwhile, heat the second skillet until almost smoking. Add the chanterelles and thyme sprigs and cook over high heat, tossing, until the mushrooms are browned, about 5 minutes; discard the thyme sprigs.
Rewarm the sweet pea oatmeal and mound on 4 large plates. Arrange the vegetable ragout and the chanterelles around the oatmeal and top each serving with 2 quail. Serve right away.