Bring large pot of water to boil over medium-high heat. Add pasta and cook al dente, according to package directions.
While pasta is cooking, in another large 12-inch pan, melt the butter and olive oil over medium-low heat. Add the garlic and saute for 1 minute (careful, garlic burns easily!). Add the shrimp, 1 tsp salt, pepper, and saute until the shrimp just turn pink, about 5 minutes, stirring often. Remove from heat and add lemon zest and lemon juice to shrimp. Toss to combine.
When the pasta is done, drain the water and put it back in the pot. Add a drizzle of oil and stir to prevent sticking. Immediately add the shrimp in lemon sauce, toss well, and serve.
Garnish with lemon slices and freshly grated Parmesan.