Heat 1 tbsp of olive oil in a medium nonstick skillet over medium heat. Add the mushrooms, onions, and garlic and cook, stirring often, until the onions are soft and golden brown, about 4 minutes. Stir in the oregano, parsley, and sea salt, turn off the heat and transfer to a medium bowl to cool.

Place the ground beef in a large bowl, add the cooled mushroom mixture, and gently fold the two together. Divide the ground beef mixture into 8 equal balls and then gently form each into semi-compact 2 1/2- to 3-inch thick patties. Split the rolls in half and brush the cut side with some of the remaining 2 teaspoons of olive oil. Set aside.

Heat a nonstick grill pan over medium-high heat for 2 minutes. Add the burgers and grill on each side until browned, about 2 minutes per side for medium. Transfer to a plate while you grill the rolls, cut-sides down, until golden and etched with grill marks from the pan, about 1 minute. Place each patty on a bun bottom and top with a slice of tomato. Spread some honey mustard on the other bun half and top of the slider.