Heat 2 tablespoons olive oil in a large lidded sauté pan over medium-high flame. Brown sausages, turning occasionally, 6 to 8 minutes. They don’t have to cook through at this point. Transfer to plate and reduce heat to medium.
Add onion, along with a little more oil, if needed. Cook, stirring frequently, until beginning to soften, about 3 minutes. Don’t brown—reduce heat, if necessary.
Add garlic and tarragon. Cook until fragrant, stirring constantly, about 45 seconds.
If you’re adding cherry tomatoes, do so now. Season with salt and pepper, stir to combine with onion mixture and cook, stirring occasionally, until some tomatoes begin to break up, about 5 minutes.
Add kale and stir to combine. Sprinkle in a little extra water and cover pan with lid. Let cook for about 2 minutes; kale will start to cook down slightly.
Meanwhile, put 1 can of drained cannellini beans into a blender or food processor. Mix wine and 1/2 cup of water in a measuring cup and add about 2/3 of it to the food processor. Process until smooth.
Add processed beans, the remaining can of whole beans and the remaining wine/water mixture to pan. Stir to combine everything. Nestle sausages into the mixture and raise heat to bring to a boil. Then reduce heat to a simmer, cover pan and cook until sausages are cooked through and flavors have combined, 7 to 10 minutes. If liquid is thickening too much, stir in a little more water.
Taste and adjust seasonings with salt and pepper (and honestly, add some more pepper for the visual effect, if for no other reason). Spoon beans into shallow bowls and top with sausages. Serve.