Step 1

Blend garlic, nuts, 1 tsp. salt, and 1 ice cube in a blender on low speed to a coarse paste. Add basil, 1 cup oil, and 2 Tbsp. ice water and purée until basil is almost incorporated. Add Parmesan and Pecorino; blend to combine. Transfer pesto to a medium bowl. Cover with plastic wrap, pressing directly onto surface.

Step 2

Cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente. Drain, reserving ½ cup pasta cooking liquid.

Step 3

Meanwhile, heat remaining 2 Tbsp. oil in a large skillet over medium heat. Cook Speck, stirring occasionally, until browned, about 2 minutes. Add shrimp; season with salt and pepper. Cook, tossing occasionally, until shrimp are just cooked through, about 3 minutes. Remove from heat; toss in pesto, pasta, and pasta cooking liquid.

Step 4

DO AHEAD: Pesto can be made 3 days ahead. Top with a little oil; cover and chill.