In a small bowl, mix together the pineapple, jalapeño pepper, cilantro, red onion, juice from 1/2 lemon and a few pinches of salt. Set aside.
Add a tablespoon of olive oil to a medium sauté pan, placed over medium heat. When the oil is hot, add the zucchini or summer squash, ancho chile powder and a few pinches of salt. Mix until combined. Cook until the squash is bright in color and a teeny-bit translucent, about 3 minutes. Mix in the squash blossoms until slightly wilted. Turn the heat off and cover the pot so the mixture stays warm.
Rub a fry pan or griddle with a 1/2 teaspoon of olive oil and heat over medium-low heat. Assemble the quesadillas, you know how to do this, place a handful of cheese between two tortillas. Cooking them in batches, transfer them to the skillet or griddle and cover them with a lid to help melt the cheese. Place the quesadillas in a warm oven while you cook the rest of the quesadillas.
To assemble, fold the quesadillas like a taco and fill them with a few spoonfuls of the zucchini mixture and top with pineapple salsa. Repeat with all of the quesadillas.