1. Place a small roasting pan in oven. Preheat oven and pan to 500°.
2. Cut tops from carrots, leaving 1 inch of greenery on each carrot.
3. Stir together olive oil and 1 Tbsp. butter in preheated pan. Add carrots, salt, and pepper; toss to coat. Bake 10 minutes.
4. Meanwhile, melt remaining 2 Tbsp. butter in a small saucepan over medium-high heat. Add shallot; sauté 1 minute. Remove from heat, and stir in bourbon and next 2 ingredients. Return to heat, and bring to a boil, stirring occasionally. Reduce heat to medium, and cook 5 minutes or until mixture is syrupy.
5. Drizzle syrup over carrots; toss to coat. Bake 5 to 7 more minutes or until carrots are crisp-tender. Transfer to a serving dish, and sprinkle with thyme.