Put the oil in a large, heavy (preferably nonstick) skillet over medium-high heat. Cut each shrimp crosswise into 3 or 4 pieces. Add to the skillet, raise the heat to high, and cook for 2 minutes, stirring once or twice. Meanwhile, core, dice, and briefly drain the tomato in a sieve or small colander. Chop the leaves from the cilantro sprigs. Remove the shrimp to a plate and place 1 tortilla in the skillet. Reduce the heat to medium.

Spread the shrimp evenly on the tortilla, crumble the goat cheese on top, then spread the tomatoes and cilantro evenly over the shrimp and cheese. Finely chop the jalapeño slices and spread on top. (If using fresh jalapeños, stem and seed them first.) Season with salt and pepper to taste. Top with the second tortilla and cook for 3 minutes. Invert a plate the same diameter as the skillet over the quesadilla, then flip the quesadilla onto the plate, cooked side up. Slide the quesadilla back into the skillet, uncooked side down, and cook for 4 minutes.

Meanwhile, peel and quarter the onion. Put in a food processor and pulse a few times to chop very coarsely. Halve, pit, peel, and quarter the avocado. Juice the lime. Add the avocado, lime juice, and salt and pepper to taste to the processor. Pulse a few times, or until the salsa is fully combined but still a bit chunky.

Cut the quesadilla into wedges--right in the pan or after putting it on a platter. Serve with the avocado salsa.