Using the same skillet that was used to cook the onions, add the remaining 2 tablespoons of olive oil over medium heat. Add the minced garlic, sliced mushrooms, black pepper, and the remaining ½ teaspoon kosher salt.
Sauté the mushrooms, stirring frequently, until they have softened and released their moisture, approximately 2–3 minutes.
Add the sliced swiss chard to the pan and cook for an additional 1–2 minutes, stirring gently, until the greens have slightly wilted. Remove the skillet from the heat and allow the mixture to cool briefly.