Begin by preheating your oven to 180FAN or 400 degreed Fahrenheit.
While the oven gets hot, prep your carrots and onion by chopping them into uniform-sized pieces, about one inch chunks.
On a baking sheet, toss the carrot, onion and garlic cloves with a generous amount of olive oil as well as the salt and paprika.
Roast the vegetables until they are deeply charred and very tender, about 35 minutes. If they aren't deeply charred after 35 minutes, leave them in the oven until they are well-roasted.
When they're finished roasting, scrape them into a blender (with the olive oil and juices on the pan) and add the chipotle: I like spice, so I add 3 whole peppers and 2 tbsp of juice. If you want a milder sauce, start with less and add more if necessary.
Add the juice of a lime and about 1/4 cup of olive oil and blend. From here, if the mixture is still pretty thick, add more olive oil until the mixture is loose enough to blend. I usually end up adding 1/2 cup olive oil total to get to my preferred consistency, which is thick and not at all runny. If you prefer a thinner sauce, continue adding olive oil and/or lime juice to achieve your desired constistency. If you add much more olive oil, remember to taste and add more salt or cumin, if necessary.
This will keep in the fridge in a sealed container for about 10 days, though mine never lasts that long. I always serve it at room temperature.
Preheat your oven to 180FAN (400 degrees Fahrenheit).
While your oven heats up, prepare your veggies by coating them in your taco seasoning and olive oil. Pop them on a baking tray and roast them until they're charred on the edges and fork tender, about 20-25 minutes.
When your veggies are almost done roasting, heat a non stick or cast iron skiller over medium-high heat and add 2 tbsp of butter to the skillet. Allow the butter to melt completely and begin to form small bubbles before moving to the next step. The butter should take about 5 minutes to reach this stage. It will be slightly golden in color and just fragrant (it will smell rich and a bit nutty, yum!) At this point, I add a few dashes of chili powder to the butter to give it even more richness and depth of flavor; plus, the color it lends the tortillas is perfection.
Place a tortilla into the buttered pan and add enough cheese to cover the tortilla. Add your veggies on top of the cheese, taking care to evenly distribute them. Cover the top with another tortilla and press the top tortilla down to secure it.
Cook the quesadilla about 3 minutes, or until the cheese is completely melted and the underside of the quesadilla is browned. Using a spatula, carefully flip the quesadilla over and cook the other side until it's browned as well. Note: The temperature of a pan increases a bit as we use it so, at this point, check if you need to turn the heat down under your pan to avoid burning the butter.
Add more butter to the pan, if necessary. and repeat the process with the remaining quesadillas and serve hot, with the hot sauce.