Melt 2 tablespoons of butter in a large cast iron skillet over medium heat.
Place the carrots in the pan in a single layer.
Add in the bourbon, ¼ cup water, and salt.
Cook the carrots, turning occasionally, until just fork-tender with slight resistance, about 12 to 15 minutes.
Add the olive oil to a griddle or grill pan over medium-high heat.
Move the carrots from the pan to the griddle and cook for about 6-8 minutes on each side, until they start to char. Keep the remaining liquid in the skillet for the glaze.
To the skillet with the remaining liquid, add the remaining 1 tablespoon butter, cayenne pepper, brown sugar, and black pepper. Cook over medium heat, stirring, until reduced to a thick glaze, 3 to 4 minutes.
Place carrots on a serving platter and brush generously with the bourbon glaze.
Garnish the carrots with fresh thyme if desired and serve.