Step 1

Cook 12 oz. medium pasta (such as rigatoni or gemelli) in a large pot of boiling salted water, stirring occasionally, until very al dente (pasta will finish cooking in sauce), about 2 minutes less than package directions. Drain, reserving 3 cups pasta cooking liquid. Reserve pot.

Step 2

Meanwhile, using tongs, cook 2 ears of corn, husked, directly over a medium-high flame on stovetop, turning often, until charred and blackened in spots, 8–10 minutes. Corn will make ferocious popping noises; don’t be alarmed. (Alternatively, prepare a grill for medium-high heat; oil grate with vegetable oil. Grill corn, turning often, until charred and blackened in spots, 8–10 minutes.) Let corn cool, then slice kernels from cobs in slabs.

Step 3

Cut kernels from remaining 4 ears of corn, husked, (you should have about 4 cups); transfer raw kernels to a blender and add 1½ cups pasta cooking liquid. Purée until very smooth, about 2 minutes.

Step 4

Melt 4 Tbsp. unsalted butter in reserved pot over medium-low heat. Cook 1 medium white or yellow onion, finely chopped, 2 large poblano chiles, halved, seeds removed, coarsely chopped, and 4 large garlic cloves, thinly sliced, stirring occasionally, until softened but without taking on any color, 5–7 minutes. Add ½ tsp. crushed red pepper flakes and ½ tsp. ground cumin and cook, stirring, until fragrant, about 45 seconds. Season generously with kosher salt.

Step 5

Add puréed corn mixture to pot along with pasta. Increase heat to medium-high and cook, stirring vigorously and adding up to ½ cup reserved pasta cooking liquid if needed, until pasta is coated in sauce and al dente, about 2 minutes. Remove from heat and add zest and juice of 1 large lime and ½ cup crumbled Cotija cheese, stirring vigorously to combine.

Step 6

Divide pasta among bowls; top with charred corn, coarsely chopped cilantro, and remaining ½ cup crumbled Cotija cheese. Serve with lime wedges for squeezing over.