Combine the shredded cheddar and Monterey Jack cheeses in a bowl and set aside. Melt 2 1/2 tablespoons of butter in a large skillet over medium heat. Add the sliced mushrooms and cook for 8 minutes, stirring occasionally, until the liquid has evaporated and the mushrooms are golden brown—this concentrates their flavor. Add the minced garlic and stir constantly for 30 seconds until fragrant. Add the fresh spinach, a pinch of salt, and black pepper, then cook for 2 minutes, stirring, until the spinach is wilted. Remove the vegetables to a plate and let them cool slightly. I like to squeeze the lime juice into the warm vegetables right after they finish cooking—it adds brightness that cuts through the richness of the cheese and chicken.

Clean the skillet and return it to medium heat. Working with one quesadilla at a time, lightly butter the pan with about 1/2 teaspoon butter per quesadilla. Place a flour tortilla in the pan and heat for 30 seconds, then flip it over. On the uncooked side, layer 2 tablespoons of the cheese mixture from Step 1, followed by a portion of the cooked vegetables and spinach from Step 1, about 3 tablespoons of shredded chicken, several slices of black olives, and a light sprinkle of cumin. Top with 2 more tablespoons of cheese. Fold the tortilla in half to enclose the filling. Cover the skillet and cook for 2 minutes until the bottom is golden and crispy. Flip carefully and cook uncovered for 2-3 minutes until the other side is golden and the cheese is fully melted. I find that covering the pan during the first side helps the cheese melt evenly while keeping the tortilla from browning too quickly.

Transfer each cooked quesadilla to a cutting board and let it rest for 1 minute—this allows the cheese to set slightly so it won't ooze out when you cut it. Cut each quesadilla into 4 wedges and serve immediately with sour cream and salsa on the side for dipping.