Rinse and dry the pork shoulder.
Cut into 3“ cubes.
Salt and pepper liberally.
Mix the oregano and the cumin with olive oil and rub all over pork.
Arrange the pork in a single layer and add enough water to just cover the meat.
Top with the onion, garlic, and jalapeno.
Squeeze over the juice of the orange and add the two halves.
Bring to a simmer over medium heat.
Skim and discard any foam that floats to the surface using a large spoon.
Simmer, skimming the surface and turning the pork pieces occasionally, until the meat is tender and just beginning to shred apart, about 2 1/2 hours. (You may need to adjust the heat to medium low to keep it at a simmer.)
Remove and onion quarters, orange and jalapeno.
Increase the heat to medium high and cook until the remaining water evaporates and just the rendered fat coats the bottom of the pan.
Reduce the heat to low and let the meat fry in the fat, turning occasionally, until browned all over, about 20 minutes.
Remove and discard any large pieces of fat and serve the carnitas in tacos, burritos, or tostadas with your desired toppings.