1. Heat a grill or grill pan
over medium-high heat. Brush the zucchini
with the oil or butter and season with salt and pepper. Grill, turning once until just soft, 3 to 4 minutes per side. Halve the grilled zucchini so they will fit into the tortillas.
2. Heat a skillet over medium heat and add about 1 tablespoon of the oil or butter. Lay a tortilla in the skillet and paint a light covering (more or less depending on your taste) of the Ancho Chile
Paste over the tortilla. Scatter or lay a slice of cheese just big enough to cover half the tortilla (about 1/2 ounce). Then add a strip or 2 of zucchini and some scallion slices and cover with another layer of cheese. Cook until the tortilla softens, about 1 minute. Fold the tortilla over into a half moon. Flip and cook on each side until golden brown and crisp
and the cheese melts, adding more oil or butter if the pan gets dry, 2 to 3 minutes per side. Repeat with the remaining ingredients.
3.Cut the quesadillas into wedges and serve with the Charred Tomato Salsa.