Dice the carrots into very small cubes (Brunoise). Finely chop the spring onions and parsley. Stir together lime juice, oil, 2 tablespoons water, salt and pepper to make a sauce. Add the diced carrots, spring onions and parsley.
Cook the peas with stock and the garlic cloves, covered, for 5-10 minutes until soft. Puree the peas (not too finely) and 2-3 tablespoons of vegetable stock with the hand-held blender and leave to cool. Grate the Emmentaler AOP using a coarse grater, mix with the peas and season to taste with salt and pepper.
Spread the pea mixture evenly on one half of each tortilla, leaving a 1.5 cm edge free. Close the tortilla and fry for 2-3 minutes on each side in a frying pan. Cut the quesadillas in half and serve with the carrot salsa.