Peel and very finely dice the potatoes. Russet potatoes (Idaho potatoes) can be used but are not recommended because they fall apart too easily. Put the diced potatoes in cold tap water to keep them from browning while you prepare the other ingredients.
Add 1 TBSP of oil to a large skillet over medium heat. When the oil is hot, add the onions and cook for 2 to 3 minutes. Add the garlic and cook one minute longer. Add the ground beef and break up the meat into small chunks. Add 1 tsp kosher salt (or ½ tsp table salt) and ½ tsp of black pepper. Brown the ground beef then drain. Using a potato masher, smash the ground beef into a very fine crumb. Drain and discard the water from the potatoes. Reduce the heat to medium-low and add the drained potatoes to the ground beef. Add ½ tsp kosher salt (1/4 tsp table salt), ¼ tsp black pepper, and 1 TBSP dried oregano. To bring out the flavor of the oregano, rub it between your fingers before adding it to the beef/potato mixture. Stir to combine. Add 2 TBSP of water to the beef mixture, cover, and very gently simmer for 15 minutes. After 15 minutes, taste the meat mixture. The potatoes may not yet be fully cooked but you may need to adjust the seasoning. At this point, I normally add another ½ TBSP of oregano and little bit more salt and pepper. The meat mixture needs to be a little on the salty side and have a robust taste of oregano or the flavors will be very muted after frying the tacos. If the meat is sticking to the skillet or the mixture seems a little dry, add another tablespoon of water. Cover and continue to gently simmer for 5 minutes longer. Uncover, stir, remove from the heat, and allow to cool for a few minutes.
I, personally, like these tacos in taco-size flour tortillas. My mother prefers them in fajita-size tortillas, which are smaller. Before filling the tacos, you need to warm the tortillas enough to make them pliable. I normally brush 5 tortillas on one side very lightly with water then place them in a stack on a clean kitchen towel then wrap the towel around the tortillas. Microwave the tortillas for 25 seconds (about 5 seconds per tortilla). This does not cook the tortillas or make them tough but provides enough heat for them to become pliable. You should adjust the cooking time for your own microwave. You can also do this in the oven (but it's a lot easier in the microwave).
Place a warm tortilla in the palm of your hand and put a couple of spoonfuls of the meat mixture in the center of the tortilla. The tortilla should be comfortably full of meat but not overly full or you will not be able to close it properly. Be sure to re-cover the other tortillas with the kitchen towel so they stay warm. If you are using a taco-size tortilla, you will need 3 to 4 spoonfuls of the meat mixture per tortilla. Gently fold the tortilla into a half-moon shape and pin the edges with toothpicks. Place the filled tacos in a single layer on a sheet pan as you prepare them. When you run out of warm tortillas, you will need to heat more in the microwave (I always do 5 at-a-time so they stay warm).
At this point, the tacos can be frozen and fried at a later date. Simple put a single-layer of tacos on a sheet pan and freeze for about 1 hour. I cover each taco in plastic wrap then place the tacos in a freezer bag. Before frying, defrost them in microwave (about 15 seconds per taco) or allow them to defrost in the refrigerator overnight.
Heat several cups of oil (I prefer peanut oil) in a Dutch oven or electric fryer. The oil will need to be about 2 to 3 inches deep. Heat the oil to 350°F Depending on the size of your fryer, you should be able to get 2 to 3 tacos in the fryer at one time. You should not remove the toothpicks prior to frying. When frying, do not overlap the tacos. When they have browned on one side, flip them over and brown the other. It should only take a few minutes to brown both sides. When the tacos are deep brown, drain them upside-down on a rack to allow excess oil to drip out.
After they have drained for a minute or two, carefully pull out the toothpicks (I use my fingers but needle-nose pliers do a good job for people with sensitive fingers). Fill the tacos with your choice of toppings.
*Some brands of flour tortillas are thicker than others. Thicker tortillas work particularly well in this recipe. Thinner tortillas break apart too easily when eating them.