Prepare a medium-hot fire in a charcoal grill with a cover, or preheat a gas grill to medium-high.
Combine the mayonnaise and roasted peppers in a small bowl and mix well. Cover and chill until ready to use.
In a separate small bowl, mash the cheese with a fork. Stir in the olives; set aside.
Pour the wine into a small, heavy fire-proof saucepan and heat on the grill until the wine begins to simmer.
Remove from the heat and add the dried mushrooms, stirring with a fork to ensure that all the mushrooms are moistened. Set the mushrooms aside to reconstitute for at least 30 minutes.
Gently squeeze the excess liquid from the reconstituted mushrooms and chop, using a chef's knife.
Transfer to a large bowl.
Add the lamb, garlic, oregano, red pepper flakes, salt, and pepper. Form into 6 equal patties in the shape of the rolls.
When the grill is ready, brush the grill rack with oil.
Place the patties on the grill, cover, and cook for 4 minutes. With a spatula, turn the patties over, and cook an additional 4 minutes, or until done to preference. During the last few minutes of grilling, place the rolls, cut side down, on outer edges of grill to lightly toast.
To assemble the burgers, spread the mayonnaise mixture over the bottom roll halves and the cheese mixture over the top halves.
Layer the bottom rolls with the patties, sopressata, spinach leaves, tomato slices, and roll tops.
