Make the salsa.
Cut the tomatos and red onions into small pieces. Mince the garlic and chile peppers into paste using the food processor; to ease the mincing, add some salt. If the salsa seems too sweet, consider adding a bit of cider vinegar or lemon or lime juice. Set aside.

Make the Quesadillas
Prepare two large frying pans over medium heat adding a bit of butter or oil; one pan is for the quesadillas and another one for the eggs. Place as many tortillas as you can into the hot quesadilla skillet. They won't fit flat and you will need to make several sets—that's okay. Twirl them around to toast them a bit all over then flip them, so that half of each is laying flat, with its other half draped over the edge of the skillet. Lay cheese over each, and let them toast. Turn the heat down a bit.

Crack the eggs into the other skillet and do not scramble; your pan will be hot enough when you have a good sizzle. Turn the heat down a bit, and dust each egg with salt, pepper, and paprika. After a couple of minutes, flip them, and cook them to your desired level of doneness. Some prefer a well done yolk.

Now add an egg or two to each tortilla, along with a bit of chopped arugula and a serving of the salsa, which you should scoop out with a fork so it drains a bit. Fold the odd end of the tortilla over the flat part, and flip. The top side should now be golden-brown. Cook until the bottom side is browned, too, and serve with more salsa.