Prepare the salsa by combining the tomatoes, garlic, jalapeños, lime juice and cilantro. Season to taste with salt and pepper and set aside to allow the flavors to blend.
Heat about 1/8-inch of vegetable oil in a large skillet over medium-high heat. Test for temperature by tossing a tiny piece of tortilla into the pan. If it sizzles around the edges, the oil is hot enough. Working in 2 batches so you don't overcrowd the pan, fry the tortilla quarters until lightly browned and crispy, about 1-1/2 minutes per side. Drain on paper towels and wipe the excess oil from the pan.
Return the pan to the stove, reduce the heat to low, and add the tortilla chips to cover the bottom. Using a slotted spoon so you don't pick up too much of the accumulated tomato juices, spoon the fresh salsa over the chips. Just let the mixture warm and soften the tortilla chips - don't stir.
Heat a little vegetable oil in a separate pan (preferably nonstick) over medium heat. Once the oil is hot, crack the eggs into the pan. You want them to be far enough apart so that they don't touch, so you may need work in 2 batches here as well. Fry the eggs just long enough to set the whites. Tilting the pan and spooning a little of the hot oil over the egg white (especially near the yolk) speeds the cooking a little and ensures that the yolk stays soft and runny.
To serve, use a wide spatula to transfer a portion of the tortilla chips and salsa to each of 4 plates. Place a sunny side up egg in the center of each, scatter about 1/2 of an avocado around the egg and top with some sliced scallions and chopped cilantro.