Add the olive oil to a large, deep skillet over medium heat. Add the onion and pepper. Cook for 5 minutes, or until the onion is translucent and both vegetables are getting soft. Stir every minute or so.
Add the garlic and mushrooms to the pan. Cook, stirring frequently, for another 5-8 minutes, or until the mushrooms have released their juices and are tender. Stir in the tomato paste and mix the ingredients well.
Add the red wine to the skillet to deglaze. Continue sautéing, stirring constantly, for another 3-4 minutes, or until the wine has almost entirely cooked off.
Add the diced tomatoes, salt, capers, and Italian seasoning to the skillet. Bring this mixture to a vigorous simmer, then turn the heat to low. Simmer, uncovered, for 5 minutes, or until the sauce has thickened somewhat.
Add the prepared soy curls to the pan. Simmer for 10 more minutes, allowing the flavors to mingle, the soy curls to become flavorful, and the mixture to thicken considerably.
Taste the cacciatore. Add a splash of vinegar, if desired. Adjust the salt and add freshly ground black pepper to taste. How much salt you add will depend on your taste and also how salty your tomatoes and tomato sauce were.
Serve the cacciatore over pasta or a whole grain, or scoop it up with fresh bread, if you like.