Bring a large pot of salted water to a boil. When the water is thoroughly boiling, add the pasta and cook according to the package directions until al dente.
Meanwhile, in a large skillet or shallow Dutch oven over medium-low heat, melt 1 tablespoon of the butter and cook the pancetta to render the fat and crisp it, about 8 minutes. Remove to a paper towel-lined plate to drain. Pour off and discard all but 1 tablespoon fat from the skillet. Raise the heat to medium and add the olive oil. When the oil is hot, add the garlic and red pepper flakes. Stir quickly and often so the garlic does not burn, 2 minutes at the most. Stir in the shrimp and continue to cook until just barely pink, another 2 to 3 minutes. Add the Fresno chiles, half of the lemon zest and the pancetta. The shrimp should be slightly undercooked.
Drain the pasta directly into the skillet and stir everything together, letting the shrimp finish cooking and the pasta absorb some of the sauce. Add the remaining zest, 1 tablespoon butter and a drizzle of olive oil. Remove from heat and add the cheese and basil. Do not stir. Serve immediately, family-style.