Heat the vegetable oil in a large saut� pan over medium heat. Add the onions, season with salt and cayenne, and cook, stirring, until they begin to wilt, about 2 minutes.
Add the beef, chili powder, cumin, crushed red pepper, and oregano, season with salt and cayenne, and cook until all the pink in the meat disappears, 5 to 6 minutes.
Add the garlic, tomatoes, tomato paste and 2 1/2 cups beef stock, bring to boil, and reduce the heat to medium-low. Simmer, uncovered, until the meat is tender, about 1 hour, stirring occasionally. Skim off any fat that rises to the surface.
Combine the masa harina flour with the remaining 1/2 cup stock and mix to blend. Slowly add to the pot, stirring to blend. The mixture will thicken. Cook for 30 minutes then season again with salt and cayenne. It should be thick enough to coat the back of a spoon.
In a heavy, deep pot or an electric fryer, heat 4 inches of vegetable oil to 360F. Fry the shoestring potatoes in batches until golden brown, 3 to 4 minutes per batch. Drain on paper towels then season with salt and cayenne.
Preheat the oven to 400F.
Cover the bottom of a large, glass rectangular baking pan with the shoestring potatoes. Combine the Cheddar and Jack cheeses. Sprinkle the cheese over the fries.
Bake just until the cheese melts, 3 to 4 minutes. Remove the pan from the oven and spoon the chili over the top of the fries. Garnish with the sour cream and jalapenos. Serve immediately.