Heat olive oil over med-high heat in a dutch oven, and sauté carrots and shallots for 5 minutes.Add wine and scrape up any bits stuck to the bottom of the pot.
Add lentils, onion, 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 min more, until liquid reduces slightly and spinach wilts. Sprinkle with crumbled feta and serve.