Heat 1 tablespoon of the olive oil in a skillet over medium-high heat. Add the onion and garlic and sauté until softened and fragrant, about 3-4 minutes.
Transfer the cooked onion and garlic to a food processor. Add the remaining 2 1/2 tablespoons of olive oil, the roasted red bell peppers, a pinch of kosher salt, and the heavy cream, if using.
Process until smooth, or pulse for a looser, slightly chunky texture, scraping down the bowl as needed. For an ultra-smooth coulis, pass the sauce through a fine-mesh sieve.
Pour the mixture into a saucepan, stir in the balsamic vinegar, and simmer over low heat for about 10 minutes, stirring occasionally, until slightly thickened.
Remove from the heat. Taste and adjust with more salt or a splash of vinegar as needed. Serve warm, or let cool, cover, and refrigerate.