Heat 1 tablespoon olive oil in a skillet over medium-high heat. Add the mushrooms and cook, stirring occasionally, until tender and golden, about 10 minutes. Season to taste with salt. Stir in the ham and sage.
Using a fine grater, grate the flesh side of the bell pepper quarters into a large salad bowl; discard any skin. Stir in the remaining 2 tablespoons olive oil, the vinegar and salt to taste. Add the spinach and toss to coat. Top with the mushroom mixture just before serving.