Preheat oven to 350°F.
For the dough: Add the flour and salt in a bowl. Make a well in the center and stir in the vegetable oil or shortening and some water.
Knead the dough until the dough becomes uniform.
Make walnut-size balls from dough and let the dough rest.
Sprinkle flour on the work surface. Roll the dough with a rolling pin up to a height of 1/8 inches. Cut dough into discs, approximately 3 inches in diameter. Set aside.
For the squash: Roast in the oven, about 45 minutes.
Remove from oven. Process the squash through a food mill.
Heat a tablespoon of olive oil in a skillet. Add the chopped onion and the jalapeño pepper.
Reduce the heat to medium and cook until the pieces are tender and translucent.
Add the crushed garlic and cook for another minute.
Stir with salt, pepper and jalapeño dry freshly ground pepper and adjust the seasoning to taste.
Add the chopped mozzarella cheese and squash puree.
Add a teaspoon of the filling onto each disc. Seal around the edges of each disc using water.
Make a decorative repulgue (it will help to keep filling from leaking).
Brush the top of each empanada with egg. Bake in oven or fry on stove until golden brown.