Cooking sausages on the top of the lentil mixture infuses this one-skillet meal with rich, meaty flavor.
Adjust oven rack to middle position and heat oven to 375 degrees. Heat oil in 12-inch skillet over medium-high heat until just smoking. Add sausage and cook until browned all over, about five minutes; transfer to plate
Reduce heat to medium, add shallots and garlic to now-empty skillet, and cook until vegetables start to brown, about 3 minutes. Add kale, broth, 1/4 teaspoon salt and 1/4 teaspoon pepper; cover and cook until wilted, about 5 minutes
Stir in lentils. Arranged browned sausage on top of lentil mixture and transfer skillet to over. Cook, uncovered, until sausage registers 160 degrees, about 12 minutes. Whisk yogurt, mustard, and water together in bowl; drizzle over top. Serve.
For a spicier kick, use hot Italian sausage.