Cook the Potatoes: Place the scrubbed new potatoes and dill sprigs in a large pot. Cover with cold, salted water. Bring to a boil and cook for 15-20 minutes, or until tender when pierced with a knife. Drain and let them cool slightly.
Prepare the Salad Base: While the potatoes are cooking, place the rinsed cannellini beans in a large bowl and roughly mash them with a fork, leaving some texture. Add the finely diced carrot, red onion, chopped dill, chives, and capers to the bowl.
Make the Sunflower Cream: Drain the soaked sunflower seeds and place them in a blender. Add 60 ml of fresh water, lemon juice, Dijon mustard, salt, and pepper. Blend until completely smooth and creamy. If the cream is too thick, add a little more water, one teaspoon at a time.
Combine the Skagen Salad: Pour the sunflower cream over the bean and vegetable mixture in the bowl. Gently fold everything together until well combined. Taste and adjust seasoning if necessary.
Prepare the Side Salad: In a small bowl, whisk together the rapeseed oil, white wine vinegar, salt, and pepper for the vinaigrette. Just before serving, toss the mixed greens with the vinaigrette.