In a large pot or Dutch oven, heat the olive oil over medium heat. Add the sliced onions and a pinch of salt. Cook, stirring occasionally, until the onions are soft and caramelized, about 20-25 minutes.
Add the minced garlic, sliced mushrooms, thyme, rosemary, and a pinch of salt and pepper to the pot. Cook, stirring occasionally, until the mushrooms release their moisture and begin to brown, about 5-7 minutes.
If using, add the white wine and cook for 2-3 minutes, scraping up any browned bits from the bottom of the pot.
Add the broth and bring to a simmer. Cook for 10 minutes.
Add the kale and cook until wilted, about 5 minutes.
Stir in the heavy cream and heat through. Do not boil.
Season with salt and pepper to taste.