Preheat oven to 400°F. Using a vegetable peeler or paring knife, cut 2 (2-inch) strips of peel from orange, including as little pith as possible. Grate remaining orange to yield 1 teaspoon zest. Juice orange to yield 1 tablespoon juice.

Melt ½ cup butter in a small skillet over medium. Once butter is melted, cook, stirring often, until solids begin to brown and butter smells nutty, about 3 minutes. Whisk in bourbon, thyme, cayenne (if using), and orange peel strips until bubbling subsides, about 20 seconds.

Transfer to a small heatproof bowl or measuring cup. Whisk in 2 tablespoons maple syrup. Let brown butter mixture cool for 10 minutes.

Slice potatoes crosswise into ⅛-inch-thick rounds (about 10 cups total). Place in a large bowl. Add shallots, pepper, 2 teaspoons salt, and ⅓ cup brown butter mixture; toss to coat. Arrange potatoes, upright, in 2 circles in a 10-inch cast-iron skillet, leaving a 2-inch gap in each circle. Push slices over so they overlap and fill in empty space in each circle. Cover skillet with aluminum foil.

Bake until potatoes are mostly tender, about 45 minutes. Uncover and brush tops with 2 tablespoons brown butter mixture. Continue baking until potatoes are fork-tender, about 20 minutes, brushing with half of remaining brown butter mixture after 10 minutes of baking. Remove from oven and brush with remaining brown butter mixture.

Meanwhile, line a large rimmed baking sheet with parchment paper. Melt remaining 1 tablespoon butter in a medium skillet over medium-low. Whisk in cinnamon, orange zest and juice, and remaining 2 tablespoons maple syrup and ¼ teaspoon salt. Add pecans and stir to coat. Cook, stirring often, until pecans are toasted, about 5 minutes. Transfer to prepared baking sheet. Let cool completely, about 30 minutes.

Serve potatoes sprinkled with glazed pecans and flaky sea salt. Make-Ahead and Storage Instructions Prepare pecans and store in an airtight container at room temperature for up to 2 weeks. Up to 2 days in advance, slice sweet potatoes and prepare brown butter mixture; refrigerate in airtight containers.