In a 4-quart or larger slow cooker set on high, pour in the vegetable stock, cover, and heat until warm, about 15 minutes.
In a medium sauté pan set over medium heat, warm the olive oil until it begins to shimmer, about 2 minutes. Add the shallots and cook, stirring, until translucent, 1 to 2 minutes. Stir in the carrot and celery and cook until they begin to soften, about 2 minutes longer. Add the thyme, paprika, and coriander, stir well, and transfer the mixture to the slow cooker.
Rinse the lentils in a fine-mesh sieve under cold running water. Add them to the slow cooker. Stir in 2 teaspoons salt or to taste, cover with the slow cooker lid, and cook on the high setting until the lentils are tender and the flavors have melded, 2 1/2 to 3 hours.
Remove the thyme sprigs. Use an immersion blender to quickly and partially blitz the soup a bit to make it a little smoother and bring it together. (Alternatively, using a ladle to transfer 1 cup of the soup to a blender, let it cool slightly, and purée it. Then return the purée to the slow cooker.)
In a large skillet set over medium-high heat, melt the butter. When the butter bubbles and froths, add the kale and cook, stirring until it has wilted, 2 to 3 minutes. Season with a pinch of salt and add the kale to the soup.
Stir in the lemon zest and sherry vinegar and season to taste with salt. To serve, garnish each bowl with a dollop of sour cream and a sprinkle of parsley.