4 tablespoons unsalted butter, melted and cooled slightly
1 teaspoon vanilla extract
½ cup whole buttermilk, room temperature
In the bowl of a stand mixer fitted with the paddle attachment, beat softened butter at medium speed until smooth, about 1 minute. Add ½ teaspoon salt and confectioners’ sugar, and beat until smooth, about 1 minute. Add egg yolk, and beat until combined, about 1 minute. Add 1½ cups flour in two additions, beating just until combined after each addition.
Turn out dough onto a lightly floured surface, and gently knead 3 to 4 times. Shape dough into a disk and wrap in plastic wrap. Refrigerate for 1 hour.
Preheat oven to 325°.
On a lightly floured surface, roll dough into an 11-inch circle, about ¼ inch thick. Transfer to a 9-inch round tart pan, gently pressing into bottom and up sides. Trim excess dough. Freeze until firm, about 10 minutes. Prick bottom of dough with a fork. Top with a piece of parchment paper, letting ends extend over edges of pan. Add pie weights.
Bake until edges look dry, about 10 minutes. Carefully remove paper and weights; bake until crust is dry and edges are golden brown, about 10 minutes more. Let cool completely on a wire rack.
Sprinkle tart evenly with coconut. Place pecans in concentric circles in crust. In a large bowl, whisk together granulated sugar, remaining 2 tablespoons flour, and remaining ¼ teaspoon salt. Whisk in eggs, melted butter, and vanilla until combined. Slowly add buttermilk, whisking until just combined, and gently pour over pecans.
Bake until the edges are set but the center still slightly jiggles, about 35 minutes. Let cool completely on wire rack. Serve warm or chilled.