Step 1

Preheat oven to 425°. Toss carrots, mushrooms, radishes, and 2 Tbsp. oil on a large rimmed baking sheet; season with salt. Roast, tossing occasionally, until lightly browned and halfway tender, 15–20 minutes.

Step 2

Meanwhile, mix peas and garlic in a medium bowl. Pour boiling or very hot water over and let stand until peas are thawed, about 5 minutes. Drain well and return to bowl. Add lemon zest, 1 Tbsp. lemon juice, 1 oz. Parmesan, and 2 Tbsp. oil. Mash well, preferably with a potato masher, until mixture is broken down and creamy; season with salt and pepper.

Step 3

Drizzle bread with oil; season lightly with salt. Toss asparagus and scallions with vegetables on baking sheet and arrange bread around the edges. Continue to roast until all vegetables are crisp-tender and browned and bread is lightly toasted, 7–9 minutes longer.

Step 4

Divide mashed pea mixture among bread slices and cut each in half. Mound roasted vegetables on top of peas. Drizzle with oil, then top with mint, more lemon juice, and shaved Parmesan.