Bring a large pot of salted water to a boil. Cook the pasta according to package directions until al dente. Reserve 1 cup of pasta water before draining.
Heat olive oil in a large skillet over medium heat. Sauté the leek until softened, about 4–5 minutes. Add the garlic, half of the peas, mixed greens, dill, salt, and pepper. Cook until the greens have wilted.
Transfer the mixture to a blender along with the vegetable broth. Blend until smooth and creamy.
While the sauce cools slightly, combine the basil, toasted pine nuts, lemon juice, garlic, salt, pepper, olive oil, and parmesan (or nutritional yeast) in a food processor. Blend until smooth, adding a little more olive oil if needed.
Return the drained pasta to the pot. Stir in the green sauce, butter, remaining peas, and a splash of reserved pasta water until glossy and well coated.
Divide among bowls and top with dollops of pesto, torn burrata, toasted pine nuts, microgreens, parmesan or nutritional yeast, and a pinch of red pepper flakes.
Serve warm beneath the spring sunshine and enjoy.