Bring a large pot of salted water to a rolling boil and cook pasta according to package directions until al dente, about 10-12 minutes. Reserve 1 cup of pasta water and drain the rest.

In a large skillet, melt two tablespoons of unsalted butter over medium heat. Add sliced leeks and minced garlic, sautéing for about 6 minutes until soft and translucent.

Stir in fresh shelled peas and cook with leeks and garlic for another 2-3 minutes until bright green. Add sea salt to enhance flavors and remove from heat.

Transfer half of the sautéed mixture to a blender. Add parsley, half a cup of reserved pasta water, and a splash of olive oil. Blend until smooth.

Return the cooked pasta to the skillet with remaining leeks and peas. Pour the blended sauce over the pasta, mixing thoroughly. Adjust consistency with more pasta water if needed.

Top the pasta with grated Parmigiano Reggiano and torn burrata. Incorporate roasted asparagus and radicchio if using, and serve warm.