Step 1

Combine squash, shallots, garlic, anchovies, oil, red pepper flakes, and turmeric in a large Dutch oven or other heavy pot; toss to coat. Place pot over medium heat, cover, and cook, stirring occasionally, until vegetables are very tender but have not taken on much color, 20–25 minutes. Transfer to a blender; reserve pot. Blend squash mixture until smooth. Season squash purée with salt.

Step 2

Cook hazelnuts and butter in a small skillet over medium-low, stirring often, until nuts are just golden, 6–8 minutes (nuts will continue to cook off heat). Season with salt.

Step 3

Cook pasta in a large pot of boiling salted water until just shy of al dente, about 1 minute less than package directions. Drain, reserving 1 cup pasta cooking liquid.

Step 4

Transfer pasta to reserved pot; pour in squash purée and ½ cup pasta cooking liquid. Cook over medium-high heat, tossing often and adding more pasta cooking liquid a tablespoon or two at a time if needed, until sauce is thickened and coats pasta, about 2 minutes. Stir in lemon juice. Taste and season with more salt if needed.

Step 5

Divide pasta among shallow bowls or mound on a platter. Top with Parmesan and basil. Spoon hazelnuts over.