In a Dutch oven, sear the ground beef in hot, bacon grease. With a slotted spoon, remove the beef, then discard most of the grease. Throw in the flour, onions, water to barely cover the meat, chile powder, cumin, Mexican oregano, tomato purée and garlic. Season to taste with salt and black pepper. Stir the pot until the ingredients are well-incorporated. Bring the liquids to a fast boil, cover the pot, cut the heat to a slow simmer and braise for 1 1/2 - 2 hours. Stir the pot - on occasion.
About 2 hours before the chili is finished, immerse the cut potatoes in a bath of cold water and ice cubes for an hour. (The cold shock liberates the starch and brings the sugars to the surface for perfect browning.) Before blanching them, drain then dry the potatoes with paper towels.
Prepare a deep fat fryer. Use peanut or safflower oil as the frying medium. Heat the oil to 260-275 degrees. Blanch potatoes in oil until they are tender. Depending on the size of your fryer, you may need to blanch and crisp in batches. Set blanched potatoes aside to drain and cool - approximately 1 hour.
When the chili is finished, crank up the deep fat fryer to 365-375 degrees. Crisp the potatoes in hot oil, until golden-brown. Drain and season with salt.
On a large platter, arrange a layer of fries, followed by chili then cheese. Repeat layering until the fries and chili are exhausted. Grate a large heap of cheese over the chili. Serve with sour cream on the side.