Make the sauce: Heat the olive oil in a medium saucepan over medium heat. Add the shallot, garlic, cumin and coriander. Cook, stirring occasionally, until the shallot softens, about 3 minutes.
Add the bourbon and cook until reduced by about half, about 1 minute. Add 1/2 cup water, the blueberries, blackberries, ketchup, 2 tablespoons brown sugar, the vinegar, soy sauce, chipotle, thyme sprigs, 1/2 teaspoon salt and 1/4 teaspoon pepper. Bring to a simmer, stirring occasionally; cook until thickened, 20 to 25 minutes. Remove from the heat and stir in the butter. Season with salt and pepper; add the remaining 2 tablespoons brown sugar if the sauce is too tart.
Meanwhile, preheat a grill to medium high. Oil the grill grates. Pat the steaks dry and season with salt and pepper. Grill until marked, 5 to 6 minutes per side for medium rare. Transfer to a plate and let rest 10 minutes.
Pour any juices from the plate of steak into the sauce; loosen with water if needed. Serve the steak with the sauce.