Preheat oven to 450°F (230°C). Thaw pizza crusts at room temperature.
Saute leek, onion, and carrots in 2 tbsp olive oil until softened, 7-9 minutes. Transfer to a plate.
Cook chickpeas in the same pan until crisp, about 5 minutes. Transfer to a paper towel-lined plate.
Make sauce by melting butter, adding garlic, herbs, and flour; whisk 1-2 minutes. Gradually add milk and broth, boil, then simmer until thickened, 5-6 minutes. Fold in vegetables, chickpeas, and peas.
Layer torn crust over sauce, drizzle with olive oil, sprinkle with salt, and bake until golden, 15-20 minutes. Cool slightly before serving.
Notes
Ensure the crust is fully covered with sauce before baking for best results.