In a large skillet, heat the EVOO over medium-high. Add the peppers, sprinkle with the salt and cook, stirring often, until the peppers are tender, about 15 minutes. Remove from the heat; stir in the garlic.
Divide the oregano sprigs between 2 pint-size canning jars. Pack the pepper mixture tightly into the jars.
In a liquid measuring cup, combine the red wine vinegar and 1/2 cup water. Pour over the peppers, making sure they're completely submerged. Screw on the lids and shake until the seasonings are evenly distributed. Let stand at room temperature 24 hours. Refrigerate at least 3 days before eating. (The pickles are best eaten within 1 month.)