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Heat oil in a small saucepan over medium heat. Add the onion and cook until tender, add in the garlic and jalapeno, sauté for 1 min.
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Add the bourbon and simmer until most of the liquid has evaporated, then stir in the vinegar, brown sugar, ketchup, water and blackberries. Return to a boil then reduce the heat and simmer, stirring occasionally, until it thickens up (approximately 10 minutes).
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Preheat grill to high.
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Rub each steak well with the oil, salt and pepper. Place the steak on the hot grill and sprinkle the thyme leaves on the top. Grill for 3 to 5 minutes, flip and grill another 3-5 mins for medium-rare.
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Remove the steaks and loosely wrap in tin foil to rest for 5 minutes. Serve with the sauce.