In a large nonstick skillet, heat oil over medium heat; swirl to coat pan. Add onion and potatoes; cook until onion is lightly browned, 8 to 10 minutes. Add mushrooms, thyme, and salt; cook, stirring often, until mushrooms are tender, 8 to 10 minutes.
Stir in tomato paste and 2 cups water; cover, and cook until potatoes are tender, 8 to 10 minutes.
Add half the spinach; cover, and cook until wilted, about 1 minute. Add remaining spinach and beans; cook, covered, until heated through. Stir in vinegar, if desired. Season with salt and pepper, and toss to combine.