For the cookies: arrange racks in upper and lower thirds of oven and heat oven to 350°F. Line 2 baking sheets with silicone liners or buttered aluminum foil.

Melt butter in a medium saucepan over medium heat. Once melted, continue to cook, stirring, until it turns nut-brown in color, about 5 minutes. Transfer browned butter to a medium bowl and stir in remaining ingredients, 1 at a time, mixing each in thoroughly before adding the next.

Spoon ½ teaspoon–size dollops of batter, spaced about 3 inches apart, onto prepared baking sheets. Bake for 8 to 10 minutes, until cookies are browned around the edges but still a shade lighter in the center. Transfer cookies (on their foil or silicone liner) to a cooling rack and cool completely.

For the filling: combine chèvre and butter in bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until smooth, fluffy, and well blended, 2 to 3 minutes. Reduce speed to low and add powdered sugar, 1 cup at a time, increasing speed once sugar is mixed in. Continue mixing until thoroughly blended. Remove bowl from mixer and stir in orange zest, ginger, nutmeg, and sea salt (if using).

To assemble: Gently lift cooled cookies off sheets and place half, bottom side up, on a work surface. Spoon about 1 teaspoon of filling onto each cookie, then top with remaining cookies, bottom side down, pressing gently to spread filling to edges of cookies.