In a large skillet, melt butter over medium-high heat. Add the shallot and cook, stirring constantly, until soft, about 2 minutes. Add the garlic and cook for 30 more seconds.
Add the shrimp to the skillet; sprinkle with Old Bay. Cook the shrimp for 5-6 minutes, flipping once, until they are opaque and cooked through. Use a slotted spoon to transfer the shrimp to a large bowl.
Add broth to the skillet, using a wooden spoon to scrape up any browned bits from the bottom of the pan. Bring to a boil over medium-high heat; cook until slightly reduced, 8-9 minutes.
Stir in chili sauce, lemon slices, Worcestershire sauce, rosemary and thyme; cook for about 30 more seconds. Remove from heat and pour the sauce over the shrimp. Serve immediately with pasta, bread or rice; garnish with fresh herbs.