Preheat oven to 450°F (230°C). Thaw pizza crusts at room temperature.
Saute leek, onion, and carrot in 2 tbsp olive oil over medium-high heat until softened, 7-9 minutes. Transfer to a plate.
Cook chickpeas in the same pan with 2 tbsp olive oil until crisp, about 5 minutes. Transfer to paper towel.
Make sauce: melt butter, add garlic, herbs, and flour; whisk 1-2 minutes. Gradually add milk and broth, bring to boil, then simmer until thickened, 5-6 minutes. Fold in vegetables, chickpeas, and peas.
Layer torn crust pieces over sauce, drizzle with olive oil, sprinkle with salt, and bake until golden, 15-20 minutes. Cool slightly before serving.
Notes
For extra flavor, add a pinch of black pepper or red pepper flakes to the sauce.