If using regular yogurt, place it in a strainer lined with paper towel and set the strainer over a bowl. Let the yogurt drain and thicken for 20 minutes.
Preheat oven to 300 degrees F. Place sunflower seeds and 1/4 teaspoon salt on a rimmed baking sheet and shake to combine. Toast seeds until aromatic, about 10 minutes. Cool and reserve.
Combine yogurt, buttermilk, lemon juice, mayonnaise, mustard, 1/2 teaspoon salt and pepper. Whisk to incorporate and reserve.
Peel tough outer layer of broccoli stalks and trim off 1/4 inch from bottoms of stalks (should be about 3/4 of a pound. tender broccoli stalks remaining). Shred stalks in food processor, then shred carrots. Combine shredded broccoli and carrots with dressing and toss to combine. Sprinkle with sunflower seeds and serve.