In a large pan with a lid over medium-high heat, add one tablespoon of the olive oil, the cipollini onions, red onions, a pinch of salt and a few grinds of pepper. Cook while tossing until the red onions caramelize and the cipollini onions become golden but are still firm, about 15 minutes. Add the remaining 2 tablespoons of olive oil, the garlic, mushrooms, yellow and red bell peppers, thyme and paprika. Season with another pinch of salt and stir to cook until mushrooms are wilted and the peppers are slightly caramelized, about 6-8 minutes.
Raise the heat of the pan and add the wine while scraping the bottom of the pan to release any bits. Allow the wine to cook until it reduces and evaporates to almost nothing, about 5 minutes.