Step 1

Toast 1/4 cup of the walnuts in a large skillet over medium heat until fragrant, about 3 to 5 minutes. Transfer to a food processor. Add basil, Parmesan cheese, lemon zest and juice, garlic, 1/2 tsp. of the salt, 1/4 tsp. black pepper, and crushed red pepper flakes.Begin blending while gradually streaming in 1/2 cup olive oil; blend until smooth. Set aside.

Step 2

Cook pasta according to package instructions in a large pot of generously salted water until al dente. Reserve 1 cup pasta cooking water before draining.

Step 3

While pasta cooks, heat remaining 2 Tbsp. olive oil in a large skillet over medium. Add zucchini and mushrooms; cook 7 to 8 minutes, stirring only occasionally, until golden brown.Add shallots and season with remaining 1/2 tsp. salt and 1/4 tsp. black pepper; cook 2 more minutes. Transfer veggies to a bowl.

Step 4

Add butter to pan, and cook until the butter is amber in color with a nutty aroma, about 2 minutes. (Note: if the butter starts to burn, reduce heat to medium-low.) Stir in walnuts, and cook until nicely toasted, about 2 to 3 minutes. Season with a pinch of salt and transfer to a bowl.

Step 5

Add zucchini and mushroom mixture back to pan (with burner still on medium heat), along with cooked pasta and pesto. Gradually stream in reserved pasta cooking water, stirring constantly, until sauce becomes glossy and begins clinging to noodles. (Start with 1/2 cup water and add more as needed - you may not use it all.)

Step 6

Plate pasta and garnish with dollops of burrata or additional Parmesan cheese, if desired. Sprinkle brown butter walnuts overtop.