In a food processor, combine almonds, garlic, and parmesan. Pulse until combined.
Add basil and pulse until combined. Repeat with kale and spinach. Add olive oil and pulse until smooth. Season with salt and pepper.
Preheat oven to 375.
Toss broccolini with olive oil and bake for 15 minutes. Season with salt and pepper.
Meanwhile, cook the pasta according to package instructions. Drain pasta, reserving 1/4 cup pasta water, and return pasta to pot.
Add peas and broccolini. Add pesto and pasta water if needed. Stir in ciliegine (mozzarella) until it begins to melt. Season with salt and pepper.