Add the basil, softened butter, garlic cloves, salt, and black pepper to a blender or small food processor. Blend until smooth and creamy. Refrigerate until ready to use.
Bring a large pot of salted water to a boil. Add the pasta and 1 tablespoon olive oil. Cook according to package directions until al dente. Drain well and set aside.
Heat a large skillet over medium heat. Add the remaining 1 tablespoon olive oil and 2 tablespoon butter. Once melted, add the shrimp and minced garlic. Cook for 3 to 4 minutes, stirring gently, until the shrimp are just opaque.
Add the smoked paprika, oregano, chili paprika, salt, and black pepper. Stir gently. Pour in the beer and lemon juice, then simmer for 2 to 3 minutes until slightly reduced.
Add the cooked pasta to the skillet or transfer everything to a large serving bowl. Spoon the garlic butter over the pasta and toss until evenly coated. Gently fold in the shrimp. Serve warm, topped with grated cheese, sesame seeds, and an extra squeeze of lemon if desired.