Preheat oven to 400 F. Toss the squash with 2 teaspoons of oil, and ¼ teaspoon of salt. Lay on a baking sheet, and bake for 20 minutes.
In a large bowl, combine the masa harina, and the remaining 2 teaspoons of salt. Add the cold water, and stir with a whisk to make the dough. When it is combined, mix with your hands until the dough is a play dough-like consistency. Roll the dough into 15 balls.
Flatten each ball into a 4-to 5-inch circle. Put a tiny scoop of squash, ½ teaspoon oof jalapeño, and handful of cheese in the center. Fold the dough in half over the filling to form a half-moon shape, then reshape the dough into a circle and flatten.
Put 1 tablespoon of oil in a large skillet, and heat to medium-high. Add around 5 pupusas to the pan, and cook for 5 to 6 minutes on each side, until browned. Serve warm with chopped cilantro, if desired.