Bring a large pot of water to boil and boil pasta according to package directions. Drain.

While pasta is cooking, heat butter and olive oil together in a large skillet over medium heat just until butter melts. Add in garlic and shallots. Cook until garlic is fragrant, about 1 minute. Add in shrimp and cook 2 - 3 minutes or just until they start to turn pink. Pour in lemon juice and wine. Scrape up any bits that have stuck to the bottom of the pan.

Reduce heat to medium low and slowly whisk in cream. Stir in lemon zest and tarragon.

Add cooked pasta to the shrimp sauce. Toss to coat. Remove from heat and allow to sit for 5 minutes. Toss once more and serve.