Curried Coconut Lentil Shakshuka

3 tablespoons olive oil
1 small onion, finely chopped
1 small carrot, finely chopped
Salt and ground black pepper, to taste
2 small garlic cloves, minced
1 tablespoon curry powder, or to taste (a salt-free mild or maharajah-style curry recommended)
1 (28-ounce) can whole tomatoes
3/4 cup dried red lentils
1/2 cup full-fat coconut milk, well-stirred
1/3 cup water, plus more as needed
Pinch or two of red chile flakes, optional
1 teaspoon red wine vinegar, or to taste
6 eggs at room temperature
For serving: chopped cilantro; warm naan (or flatbread or pita)

Heat oven to 375° F.
In a 10 to 12-inch skillet over medium heat, warm the olive oil. Add the onions, carrots, and 1/2 teaspoon kosher salt, and sauté until tender, about 8 minutes, stirring occasionally. Add the garlic and sauté for another minute, then the curry powder. Cook for 30 seconds, stirring constantly, or until the curry is fragrant.
Add the tomatoes with their juice (tip: If using whole tomatoes, use kitchen shears to cut the tomatoes into small pieces once they’re in the skillet), lentils, coconut milk, water, and 3/4 teaspoon of salt. Bring to a boil, then lower heat to maintain a simmer. Cook for about 20 minutes, or until the lentils are tender, stirring frequently and scraping the bottom the pan so the sauce doesn’t stick; add a little extra water if needed. The finished sauce should be thick like a marinara sauce, with only a tablespoon or two of liquid left. Add red wine vinegar, salt, and pepper, to taste. Add chile flakes if you’d like more heat.
With the back of a spoon, make six small indentations in the sauce and crack the eggs into each one. Season the eggs with salt and pepper. Transfer pan to oven. Cook for about 7 to 10 minutes, until the egg whites are fully cooked and the yolks are still runny or more set, depending on preference.
Remove from oven. Sprinkle with cilantro, and serve with warm naan.