4. Make the Garlicky Browned Butter
While the lobsters are cooking, melt the salted butter in a medium saucepan over medium heat, stirring occasionally. Add several large grinds of black pepper and continue to cook, stirring frequently, until light brown specks start to form and the butter smells nutty, 5 to 8 minutes. Turn off the heat, add the sage, thyme, lemon zest, and grated garlic, and cook for 1 minute in the residual heat. Be careful during this step because the mixture will get quite foamy and might sputter. Season to taste with salt and pepper.