Tarte Tropézienne

Name: Tarte Tropézienne
Ingredients: 2 1/2 teaspoons active dry yeast; 1/3 cup (80 milliliters) warm whole milk (see yeast package for exact temperature); 2 cups (272 grams) all-purpose flour; 3 tablespoons sugar; 2 large eggs, at room temperature, lightly beaten; 1/2 teaspoon fine sea salt; 2 teaspoons dark rum or kirsch (optional); 1 teaspoon pure vanilla extract; 7 tablespoons (3 1/2 ounces; 99 grams) unsalted butter, at room temperature; 1 1/2 cups (360 milliliters) whole milk; 4 large egg yolks; 1/3 cup (67 grams) sugar; 1/4 cup (32 grams) cornstarch; Pinch of fine sea salt; 1 tablespoon pure vanilla extract or 1 tablespoon orange-flower water, plus 1 teaspoon pure vanilla extract; 3/4 stick (6 tablespoons; 3 ounces; 85 grams) unsalted butter, cut into bits, at room temperature; 1/4 cup (60 milliliters) very cold heavy cream; 1 large egg, for glazing; Pearl sugar or crushed sugar cubes, for finishing