Melt the butter in a large pot or Dutch oven over medium heat. Add the onion and cook for 4–5 minutes, stirring occasionally, until softened.

Stir in the garlic, paprika, salt, and pepper. Cook for 1 minute, until fragrant.

Sprinkle the flour over the onion mixture and stir constantly for 1 minute, being careful not to let it burn.

Slowly whisk in 2 cups of the chicken broth, reserving the remaining ½ cup. Slowly add the milk, then stir in the Dijon mustard.

Bring the soup to a gentle simmer, then add the carrots and broccoli. Reduce the heat to medium-low, cover, and cook for 12–15 minutes, stirring occasionally, until the vegetables are tender and the soup has thickened.

While the soup simmers, add the cottage cheese and reserved ½ cup of chicken broth to a blender. Blend until completely smooth.

To temper the cottage cheese mixture, add about ½ cup of the hot soup to the blender and blend or mix by hand until combined. Repeat with another ½ cup of hot soup, then blend or mix once more until smooth.

Remove the pot from the heat and slowly stir the tempered cottage cheese mixture into the soup until well combined. For a smoother soup, use an immersion blender to blend part of the soup, leaving some broccoli and carrots in small pieces for texture. We prefer to skip this step and keep the soup chunkier.

Add the shredded cheddar a handful at a time, stirring until melted and creamy. Taste and adjust the seasoning with additional salt and pepper as needed. Serve warm.