Clean your portobello caps by removing stems and scraping out the dark gills with a spoon. Pat dry with paper towels. In a large bowl, whisk together balsamic vinegar, olive oil, minced garlic, soy sauce, brown sugar, thyme, smoked paprika, salt and pepper to create your marinade.

Place mushroom caps gill-side up in a shallow dish and pour marinade over them, making sure to coat both sides. Let them marinate for at least 30 minutes at room temperature, or up to 2 hours in the refrigerator for deeper flavor penetration.

Fire up your grill and set up a two-zone cooking area. For charcoal, bank coals to one side for direct high heat around 450-500°F. For gas, set one side to high and the other to medium. Clean and oil your grates well to prevent sticking.

Remove mushrooms from marinade and reserve the liquid for basting. Place caps gill-side down on the hot side of the grill first. Cook for 4-5 minutes without moving them to develop good grill marks and caramelization.

Flip the mushrooms carefully with tongs and move to the medium heat zone. Cook gill-side up for another 3-4 minutes, basting with reserved marinade. The caps should feel tender when pressed but not mushy. If adding cheese, place slices on top during the last minute of cooking.

Remove mushrooms from grill and let them rest for 2-3 minutes before serving. This allows the juices to redistribute just like resting meat. Lightly toast your buns on the grill for 30 seconds if desired, then assemble your burgers with your favorite toppings.