Heat oven to 500°F with racks set in middle and lowest positions.

Toss sprouts with 2 tablespoons oil to evenly coat; season with salt and pepper. Transfer sprouts to a baking sheet and arrange cut side down in a single layer. Tightly cover sheet with foil and roast 10 minutes on lowest rack. Remove foil from sheet and continue to roast on lowest rack 7–10 minutes more until sprouts are deep golden brown.

Mound anchovies, garlic, and ¾ teaspoon salt on a cutting board. Using chef’s knife, mince the anchovies, garlic and salt together until well combined. Continue to work mixture, mashing and scraping with the side of the knife, until a smooth paste forms.

Whisk tahini, lemon juice, and Dijon in a large bowl. Place the bowl on a damp kitchen towel or paper towel to hold in place.

Start slowly dripping oil into tahini mixture while whisking constantly and vigorously. Continue, slowly adding oil and whisking vigorously, until mixture looks slightly thickened and glossy. Continue to gradually add oil in a slow, steady stream until all oil has been added and mixture looks like mayonnaise.

Add a dash of water and whisk, adjusting with more water as needed, until dressing is the consistency of heavy cream. Add anchovy mixture and Parmesan and whisk until smooth. Season with salt and pepper to taste.

Transfer cooked Brussels sprouts to bowl with dressing and toss to coat.

For the breadcrumbs, toss bread pieces with 1 tablespoon oil and season with salt and pepper; arrange in a single layer on sheet pan. Roast on the middle rack until golden brown and crunchy, about 5 minutes.

Transfer dressed Brussels sprouts to a serving platter and top with breadcrumbs and sunflower seeds.