Heat oven to 400° F. Heat 1 tablespoon of the oil in a medium ovenproof nonstick skillet over medium-high heat. Add the onion and ½ teaspoon each salt and pepper and cook, stirring occasionally, until golden brown, 3 to 4 minutes.
Add the spinach and cook, tossing, until wilted, 1 to 2 minutes. Add the eggs and sprinkle with the goat cheese. Cook until the mixture begins to set around the edges, 1 to 2 minutes. Transfer to the oven and bake until set, 10 to 12 minutes.
Whisk together the vinegar, remaining 2 tablespoons of oil, and ¼ teaspoon each salt and pepper in a large bowl. Add the greens and toss to combine. Serve with the frittata and bread.