Rinse shrimp with cold water and pat very dry with paper towels. Melt 2 tablespoons of butter in a large skillet.
Add shrimp to pan and saute 4-6 minutes over medium-high heat until opaque. Transfer to a plate and cover to keep warm.
Add remaining 1 tablespoon butter to the pan. Once melted, stir in garlic for one minute until fragrant.
Whisk in chicken broth, then gradually whisk in heavy cream. One sauce is thickened and creamy, reduce heat to low and stir in lemon juice.
Return shrimp to the pan, toss to coat in the sauce. Stir in dill and garnish with cracked black pepper. Serve immediately.