Combine the basil, butter, 2 garlic cloves, salt, and pepper in a blender.
Blend until the mixture is smooth.
Refrigerate the garlic butter while you continue preparing the remaining ingredients.
Bring a pot of water to a boil.
Add the pasta and 1 tbsp of olive oil.
Cook the pasta according to the package directions until al dente.
Heat a pan over medium heat. Melt the 2 tbsp of butter and 1 ½ tbsp of olive oil.
Add the shrimp and the minced 1 garlic clove. Cook for 7-8 minutes.
Stir in the spices: smoked paprika, oregano, and black pepper (and chili paprika, if using). Cook for an additional 4-5 minutes, stirring very gently.
Pour in the beer and 1 tbsp of lemon juice. Allow the mixture to simmer until the liquid has slightly reduced.
Drain the cooked pasta well.
In the pot, toss the drained pasta with the chilled garlic-basil butter, mixing thoroughly until the pasta is completely coated.
Gently fold in the cooked shrimp mixture.
Serve immediately on plates, garnishing with the Parmesan cheese, sesame seeds, and a final squeeze of fresh lemon juice.