Preheat toaster oven to 350 degrees F. Place garlic cloves into the oven and allow to roast 30 minutes or until garlic is softened.
While garlic is roasting, turn on your conventional oven to broil or highest heat setting. If you do not own a toaster oven, roasted the garlic first and then broil the tomatoes afterward.
Slice tomatoes and place onto a baking sheet. Season with olive oil and salt. When oven has pre-heated, place tomatoes in the oven 6 inches from broiler. Broil for 15-20 minutes or until the top of the tomatoes have a golden brown crust.
Prepare burger patties. Use a food processor to pulse crimini mushrooms until they are finely minced, about 10 seconds. Add minced mushrooms and rosemary to ground beef. Mix until just incorporated, but do not over-mix.
Form 2 burger patties. Make them slightly bigger than your burger buns, as burger patties shrink during cooking. Make burger patties approximately 3/4 inch thick on the edge, with the center slightly thinner than the edges. This will allow space for the center to rise during cooking.
Season both surfaces of the burger patty with salt and pepper. Set aside.
Take broiled tomatoes out of the oven and set aside.
When roasted garlic is softened, remove from oven. Wait until they cool ~10 minutes. When garlic has cooled enough to handle, squeeze roasted garlic out of their paper skins.
Combine roasted garlic with romesco sauce ingredients: roasted bell pepper, sun dried tomatoes, toasted almonds, olive oil, salt, smoked paprika, cayenne pepper, lemon juice, and red pepper flake. Using a food processor, blend until the sauce is smooth like the texture of pesto. Scrape down the sides for even blending. Set aside.
Heat a cast iron skillet on high until it just begins to smoke. Turn the heat to medium and drizzle in olive oil. Place burger patties into the cast iron skillet. Cook burgers 2 1/2 minutes on each side for medium rare and 3 minutes on each side for medium, flipping only once. If your burger patties are thicker than 3/4 inch, they may need extra cooking time.
Flip burger patties once a golden brown crust has formed at the bottom of the patties. After flipping the burger patties, place provolone cheese slices on top and cover with a lid for the remaining 2 1/2 minutes-3 minutes of cooking. This will melt the cheese.
When burger patties are done and cheese has melted, set aside.
Dress arugula with lemon juice and black pepper.
Assemble the burgers. For each burger, spread 2 tbsp of the romesco sauce onto the bottom bun. Then place the burger patty on top of the romesco sauce. Place 2 slices of roasted tomato on top of the burger patty, followed by arugula salad. Finally place the top bun and enjoy!