Slice the peppers: cut the top off and remove the seeds. Cut each side off of the ribs and cut crosswise into slices, about ¼-inch wide.
Slice the onions: Cut off the stem end. Cut the onion in half lengthwise (from stem to root). Remove the paper skin. Place the cut side face down and slice crosswise into slices. For larger onions, make another lengthwise cut (without cutting through the root) and then make crosswise slices.
Heat a cast-iron skillet over medium-high heat. Add the oil and the sliced onions and peppers. Season with salt and oregano.
Cook for 8-10 minutes, stirring occasionally until the veggies are slightly charred and are crisp-tender. Taste for seasoning and add more salt and oregano if desired.
It's best to serve the veggies immediately after cooking so they retain their crisp-tender texture. But you can certainly prep the peppers and onions ahead of time and store in the refrigerator for 1-2 days.