To prepare sauce: Heat oil in a small saucepan over medium heat. Add onion and cook, stirring occasionally, until tender and just starting to brown, 2 to 4 minutes. Add garlic and jalapeno and cook, stirring, until fragrant, about 30 seconds. Add bourbon, increase heat to high and bring to a boil; cook until most of the liquid has evaporated, 2 to 5 minutes. Stir in blueberries, ketchup, vinegar, brown sugar, molasses and allspice; return to a boil. Reduce the heat and simmer, stirring occasionally, until thickened, 15 to 20 minutes.

Preheat grill to high.

Combine thyme, oil, salt and pepper in a small bowl. Rub the mixture on all sides of steaks. Grill the steaks 3 to 5 minutes per side for medium-rare. Let the steaks rest for 5 minutes before serving with the sauce.