Preheat oven to 375 degrees. Toss together 3/4 cup Parmesan, 1/2 teaspoon salt, 1/2 teaspoon pepper, and cayenne in a small bowl. Toss bread with 2 tablespoons oil on a rimmed baking sheet, spread into a single layer, and sprinkle with half of cheese mixture. Bake 10 minutes. Flip bread with a spatula and sprinkle with remaining cheese mixture. Bake until bread is golden brown but still soft in center, about 5 minutes more. Reserve any cheesy bits on baking sheet.
Combine lemon zest and juice, 1/4 cup oil, 3/4 teaspoon salt, and 1/2 teaspoon pepper in a large bowl. Working with 1 artichoke at a time, peel tough outer leaves. Trim 1 1/2 inches from top and trim stem. Trim fibrous green skin from base and sides. Thinly slice each artichoke lengthwise, adding it to the bowl with dressing and tossing (this prevents discoloration). Add remaining 1/2 cup cheese and croutons, and toss to combine. Let stand until bread is slightly softened, about 10 minutes.
Just before serving, add pea shoots, radishes, and cheesy bits from baking sheet. Drizzle with remaining tablespoon oil and more lemon juice; season with salt and pepper.