Heat the olive oil in a medium saucepan over medium heat.
Add the carrot, onion, and garlic and sauté for 5 to 7 minutes, until soft and lightly browned.
Add the lentils, broth, and bay leaves.
Simmer for about 20 minutes, until the lentils are tender and the liquid has mostly evaporated.
Before serving, add the vinegar, season with salt and pepper, and discard the bay leaves.
While the lentils simmer, roast the salmon: Season the fish with salt and black pepper.
Combine the mustard and brown sugar in a mixing bowl and spread evenly over the salmon fillets.
Place the salmon on a baking sheet and place on the top rack of the oven. Roast for 8 to 10 minutes, until the salmon has browned on the surface and flakes with gentle pressure from your finger.
Divide the lentils among 4 plates or pasta bowls and top each serving with a piece of salmon.
