Wash the bell peppers, remove the stems, cut each in half, and scrape out the seeds and white ribs. Slice into strips about 1/2 inch wide.
Peel the yellow onion, cut it in half from root to tip, and slice into half-moons of similar thickness. Peel and mince the garlic.
Measure the oregano, basil, salt, black pepper, and red pepper flakes into one small bowl. Chop the fresh parsley and set aside.
Place a large skillet over medium-high heat and add the olive oil. Wait until the oil shimmers, about 1 to 2 minutes.
Carefully add the sausage links in a single layer with a little space between each one. Cook for 6 to 8 minutes, turning with tongs every couple of minutes, until all sides are deeply golden brown. Transfer to a plate and leave the drippings in the pan.
Reduce the heat to medium and add the sliced onion to the same skillet. Stir and scrape the bottom of the pan as the onions soften, about 3 minutes.
Add the pepper strips and stir to coat them in the drippings. Cook for 5 to 6 minutes, stirring often, until the peppers are just tender and the onions look golden at the edges.
Push the vegetables to the sides of the pan and add the minced garlic to the open center. Cook for 30 seconds, stirring, until fragrant.
Sprinkle in the seasoning mix of oregano, basil, salt, black pepper, and red pepper flakes. Stir everything together for another 30 seconds so the herbs bloom in the warm oil.
Pour the white wine into the skillet, or use chicken broth if you prefer. Use a wooden spoon to scrape up all the browned bits from the bottom of the pan. Let the liquid bubble for about 2 minutes so the alcohol cooks off and the sauce reduces slightly.
Nestle the browned sausage links back into the skillet, tucking them into the peppers and onions. Spoon some of the vegetables and pan juices over the top of the links.
Reduce the heat to low, cover the skillet with the lid, and simmer for 12 to 15 minutes. Turn the sausages once halfway through so they cook evenly.
Insert an instant-read thermometer into the thickest part of a sausage link. It should read 160°F. If needed, cover and cook for another 2 to 3 minutes, then check again.
If the sauce looks too thin, remove the lid and simmer for 2 minutes to thicken slightly. Turn off the heat and let the skillet rest for 5 minutes.
Top with the chopped parsley and serve hot, either whole or sliced on the diagonal.