In a large skillet over medium heat, melt the butter.
Add the grated garlic, lemon zest, lemon juice, and a generous pinch of salt and pepper.
Toss in a few sprigs of tarragon and let them infuse the butter for 1 to 2 minutes.
Add the shrimp and cook, stirring occasionally, until just pink and opaque, about 3 to 4 minutes depending on size.
Remove from heat, discard the tarragon sprigs, and let the shrimp cool slightly.
Once cooled, chop into 1-inch pieces.