2 small fresh poblano chiles
1/2 cup loosely packed fresh cilantro
1 Tbs. plus 2 tsp. vegetable oil
1/2 large white onion, thinly sliced lengthwise (about 1-1/2 cups)
Kosher salt and freshly ground black pepper
Four 8-inch flour tortillas
2 cups grated Monterey Jack cheese (about 8 oz.)
1/2 cup sour cream

Roast the peppers: Turn a gas burner to high and char the poblanos directly over the flame, turning them with tongs as soon as each side becomes fully blackened, about 6 to 8 minutes per pepper. (If you don’t have a gas stove, you can char poblanos similarly over a hot grill fire or lay them on a foil-lined baking sheet and char them under a hot broiler, turning them with tongs). Immediately after roasting, put the poblanos in a bowl, cover, and set aside to steam and loosen the skins. When they’re cool enough to handle, peel the charred skin off with your hands or a small paring knife. Pull out and discard the stems and seed clusters. Slice the peppers into 1/4-inch-wide strips and put them in a small bowl. Put a baking sheet in the oven and heat the oven to 150°F (or its lowest setting).

Make the rajas: Heat 1 Tbs. of the oil in a 10- or 12-inch nonstick skillet over medium-high heat. Add the onion and cook, stirring frequently, until soft and lightly browned, 3 to 5 minutes. Add the poblano strips, season with a generous pinch of salt and a few grinds of pepper, and cook, stirring occasionally, until the peppers are heated through, another 1 to 2 minutes. Transfer to a plate and wipe the skillet clean.

Make the quesadillas: Heat 1/2 tsp. of the oil in the skillet over medium-high heat until hot. Add one tortilla and scatter over it a quarter of the cheese, a quarter of the poblano mixture, and a quarter of the cilantro. When the tortilla smells toasty and the bottom is browned in spots, in 1 or 2 minutes, fold it in half, pressing it with a spatula to flatten it. Transfer to the baking sheet in the oven to keep warm. Repeat with the remaining ingredients to make three more quesadillas. Cut each quesadilla into wedges and serve with the sour cream on the side.