1. Heat olive oil over medium-high heat in a Dutch oven, and sauté carrot and shallots for 5 minutes. Add wine and scrape up any bits stuck to the bottom of the pot.
2. Add lentils and onion to the pot along with broth, salt, pepper, and thyme, and bring to a boil. Reduce heat to medium-low and cover tightly. Cook for 35 minutes, stirring twice, until lentils are tender and liquid is almost evaporated. Stir in vinegar and spinach, and simmer uncovered for 5 more minutes, until liquid reduces slightly and spinach wilts. Sprinkle with crumbled feta and serve.