Heat a Duch oven or large deep skillet over medium-high heat. Once the pan is hot, add the canola oil. When the oil is hot, add the onion, carrots, and celery. Turn the heat down to medium and cook, stirring often, for about 5 minutes or until vegetables are starting to soften. Add the garlic, give it a good stir, and cook until garlic is fragrant, about 30 seconds.
Add the rosemary, thyme, bay leaf, smoked paprika, salt, lentils, and chicken broth. Bring to a boil, then reduce heat to low and simmer, uncovered, for about 30 minutes. During this cooking time, you can cook the sausages.
Once the chicken broth is mostly absorbed by the food in the skillet, stir in the Dijon mustard and red wine vinegar. Remove from heat and let stand for about five minutes. To serve, scoop the lentils on a serving platter and top with the sliced sausages. Sprinkle with Parmesan cheese, rosemary leaves, or chopped flat-leaf parsley for garnish, if desired.
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