Preheat the oven to 400℉ and line a baking sheet with parchment paper.
Add the honey, butter, oil, brown sugar, lemon juice, salt, and pepper to a small saucepan and heat over low, stirring occasionally until everything is melted and well combined. Set aside to cool.
Peel your carrots and place them on the prepared baking sheet. Note: if your carrots are more than 2 inches thick, slice them into sticks that are 2 inches thick or smaller.
Pour the glaze over the carrots, then toss them to coat and place them in a single layer on the sheet pan. Sprinkle with the fresh thyme and bake in the preheated oven for 25-30 minutes, or until they are softened and slightly browned.
Transfer the warm carrots to a serving platter and garnish with more thyme and/or honey. Serve!