Arrange a rack in middle of oven; preheat to 425°F. Brush a foil- or parchment-lined baking sheet with butter; set springform ring on top. Toast caraway in a small skillet over medium heat until fragrant, about 1 minute. Let cool. Place in a resealable plastic bag; crush with a rolling pin or bottom of a skillet. Place in a large bowl. Add duck fat, 2 tablespoons butter, 1 teaspoon salt, and pepper. Add potatoes; toss to coat. Arrange 1/4 of potatoes in an even layer inside ring on baking sheet, overlapping as needed. Toss onion in a large bowl with 1 tablespoon melted butter. Arrange 1/3 of onion over potatoes. Repeat layers twice more, finishing with a layer of potatoes. Carefully remove ring. Bake until potatoes are tender, about 45 minutes. Brush with 1 tablespoon butter. Bake until edges of potatoes are deep golden and top is crisp, 5-10 minutes longer. Run a thin spatula under galette to loosen from foil. Slide onto a platter. Season with salt, if desired.