In the bowl of a stand mixer fitted with the paddle attachment, beat softened butter, confectioners’ sugar, and zest at medium speed until creamy (3 to 4 minutes) stopping to scrape sides of bowl. Beat in egg. 

Whisk together flour and salt in a separate bowl. Add the flour and salt to the creamed butter and sugar, beating just until it comes together.

Shape dough into a long rectangle and wrap in plastic wrap. Refrigerate for at least 2 hours.

In a medium saucepan, heat butter and vanilla extract over medium heat. Cook until butter turns a deep amber color and has a nutty aroma, about 10 minutes. Remove from heat.

In a large bowl, whisk together sugar, flour, and eggs. Slowly drizzle a little bit of the hot butter mixture into egg mixture, whisking constantly (doing this makes sure that you don't cook the eggs with the heated butter). Slowly drizzle in more and more of the hot butter mixture, whisking constantly. Let cool to room temperature. Once mixture is cool, whisk once more before transferring to an airtight container. Refrigerate for at least 8 hours.

On a lightly floured surface, roll the chilled dough so that it's ~1" larger than the tart pan. Transfer dough to the tart pan, pressing into bottom and up sides. Trim excess dough. Transfer tart shells to prepared pan, and freeze for 30 minutes.

Spoon the brown butter filling into the prepared tart shell. Carefully place the shingled sliced rhubarb on top of filling, and sprinkle with sugar and orange zest.

Bake until filling is set and crust is golden brown, 18 to 20 minutes. Let cool in pan completely before carefully removing.