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.
1. Stem, seed and pull the chiles in half. Toast the pieces in a dry skillet over medium heat, turning until fragrant and blistered but not charred, about 1 minute. Transfer to a bowl of boiling water and set aside to soften, 30 to 40 minutes.
2. Put the chiles in a blender with the salt (not a food processor, it won't be fine enough) and puree until very smooth. Add some of the soaking water, about 1/2 cup, if needed to engage the blender. Strain if desired.
3. Heat the olive oil in a medium skillet over medium heat. Add the paste and fry, stirring with a wooden spoon, until the mixture is thick, 3 to 5 minutes. Cool and store in the refrigerator for up to 1 month. Makes 1 1/2 cups.
1. Position rack in the upper part of the oven and preheat the broiler. Line a small broiler pan with foil.
2. Place the tomatoes and jalapeno in the pan and broil, turning them as needed, until the skins blacken and split, 15 to 20 minutes. Wrap completely in aluminum foil and cool.
3. Core the tomatoes and stem the jalapeno (remove the seeds if you want to temper the heat). Puree the tomatoes, skins and all, with the jalapeno, oil, garlic and scallions and in a blender to make a smooth sauce. Pulse in the cilantro. Transfer the sauce to a bowl and stir in 1/2 teaspoon salt. (The salsa thickens a bit if prepared ahead and chilled; stir to loosen it up before serving.) Makes about 1 1/2 to 2 cups.