Preheat the oven to 450˚F.
Halve the squash, scoop out the seeds and place on a parchment-lined baking sheet.
Drizzle with oil, sprinkle with salt and roast for 45-60 minutes, depending on the type and size of the squash, until tender and turning golden.
Meanwhile, set a heavy skillet over medium-high heat and add about half an inch of canola oil.
When the oil is hot—the edge of a tortilla should sizzle when dipped in—fry the tortilla wedges for 1-2 minutes, turning with tongs or a slotted spoon as needed, until golden and crisp.
Transfer to a paper towel-lined plate.
In a blender, pulse the cilantro, lime juice, jalapeño, garlic, mayonnaise and a pinch of salt until smooth.
To assemble the tostadas, spoon some soft roasted squash onto each tortilla, top with cojita cheese, onion and cilantro sauce.