Preheat the oven to 425°. In a large bowl, toss the potatoes with 2 tablespoons of the oil and season with salt and pepper. In a lightly oiled 10-inch nonstick ovenproof skillet, arrange one-third of the potato slices in an overlapping circular pattern. Top with half the goat cheese and another third of the potatoes. Repeat with the remaining goat cheese and potatoes.
Cut out a 10-inch round of parchment or wax paper. Moisten the paper and then lay it on top of the potatoes. Cover with a lid that fits inside the skillet and cook the galette over moderate heat for 8 minutes, or until golden around the edges when the paper is peeled back. Transfer the covered skillet to the oven and bake for 15 minutes, or until the potatoes are just tender when pierced with a knife. Remove the lid and parchment and bake for 7 minutes longer, or until the top is browned. Run a spatula around the edge of the skillet and shake to loosen the galette. Invert a plate over the skillet, flip and turn out the galette.
Heat the remaining 1 tablespoon of olive oil in the skillet until shimmering. Add the fennel pollen and a pinch of salt and cook over high heat until fragrant, about 30 seconds. Cut the galette into wedges and drizzle with the fennel-pollen oil.