In a small bowl, stir together the tomatoes, onion, jalapeño, lime juice, cilantro, and olive oil. Season with salt and pepper. Set the salsa aside.
Preheat the oven to 400°F. Prepare 2 baking sheets, one lined with paper towels and the other with aluminum foil.
Pour at least 2 inches of a neutral oil into a large pot fitted with a deep-fry thermometer. Heat to 350°F over medium-high heat. Working in batches, add the matzo pieces and fry until evenly golden brown, about 1 minute. Place on the paper towel–lined baking sheet to drain and season with salt.
Transfer the fried matzo to the foil-lined baking sheet and cover with the grated cheese. Bake until the cheese melts, 5 minutes.
Transfer the nachos to a large platter and top with the tomato salsa, pickled jalapeños, avocado, cilantro leaves, and sour cream. Serve.
Recipe Notes
For a lighter twist on a classic pairing, substitute Greek yogurt for sour cream.