Vegetables, smoky-sweet from the grill and zingy with lime juice, transform simple cheesy tortillas -- comfortingly familiar to children -- into something sublime. Other fresh, seasonal, vegetables, such as eggplant or fennel, would make a lovely addition to the line-up here. And do try to hunt down the chipotle peppers, which add their own delicious hit of smokiness: they're available canned, in the Mexican foods aisle, and you can puree the entire can and store it in a jar in the refrigerator for instant flavor-boosting. (But if your kids are spice-shy, stick with the paprika.)
Preheat your grill on high.
Whisk together the lime juice, olive oil, chipotle or paprika, salt, and garlic. Arrange the vegetables in a single layer on a large, rimmed baking sheet, and pour half the dressing over them, turning them to coat the slices evenly.
Turn the grill down to medium-low and roast the veggies, turning them and adjusting the heat as necessary, until they are completely tender, 10-12 minutes. Remove them to a plate, dress with the remainder of the lime juice mixture, and set aside.
Heat a large griddle (or a heavy frying pan) over medium-high heat, and lay half of the tortillas into it (if you're using a pan, you'll need to do this in batches). Divide the cheese over them, top with the remaining tortillas, and cook until the bottoms are golden and crisp. Flip them, and cook until the tortillas are crisp and the cheese is melted.
Open the quesadillas and divide the cilantro and grilled veggies among them, cutting the vegetables as necessary to fit, then quarter the quesadillas and serve with sour cream and salsa.