Prick the sausages all over with a fork.
Heat the olive oil in a large skillet over medium-high heat.
Brown the sausages all over, 5 to 6 minutes, and remove them to a plate.
Add the onions, peppers, and garlic to the skillet; season lightly with salt.
Cover, reduce the heat to medium, and cook until the peppers are wilted, about 8 minutes.
Make a space in the pan, and add the tomato paste there.
Toast the tomato paste in that spot for a minute; then stir it into the vegetables.
Add the white wine, and bring it to a simmer.
Add back the sausages, and adjust the heat to a gentle simmer.
Simmer, turning the sausages occasionally, until they are cooked through, 8 to 10 minutes.
Increase the heat to reduce any juices in the pan and glaze the sausages.
Stir in the basil, and serve.