Make the sauce. In a small saucepan, heat oil. Add onion and garlic. Stir until translucent. Stir in the rest of the ingredients. If the mixure is not already bubbling, increase heat. As soon as it bubbles, reduce to a simmer. Let it reduce and thicken (5-10 minutes), stirring occasionally. Taste and adjust seasonings to your liking - sweetness, spice level, salt, etc.
Depending on the size of your portobello's, either trim to fit the size of your slider bun, or cut into strips. (To make slider-sized burgers and not waste mushroom scraps, we made some of both - cut squares like the one pictured, and made others with mushroom strips).
Liberally brush both sides of the mushrooms with the sauce and let them marinade for at least 15 minutes, up to 30.
Heat oven grill or BBQ, cook mushrooms, flipping halfway through. (the time will completely depend on the heat of your grill). Grill should be a few minutes per side,
When mushrooms are done cooking, brush with more sauce and serve with whatever toppings you like.