In a small saucepan, whisk together the flour and milk until smooth with no lumps. Cook over medium heat, whisking constantly, until the mixture thickens to a paste that leaves visible lines when you whisk through it (2-4 minutes). Transfer to a small bowl and let cool to room temperature.

In a small bowl, whisk the warm milk and sugar until dissolved. Sprinkle yeast over top and let sit for 5 minutes until foamy.

In the bowl of a stand mixer fitted with the dough hook, combine the cooled tangzhong, milk-yeast mixture, melted butter, vanilla bean paste, 2 eggs, and all-purpose flour, bread flour, and salt. Mix on low speed until a soft dough forms.

Knead on medium speed for 5-8 minutes until the dough is smooth and elastic. Gradually add the softened butter, one tablespoon at a time, until fully incorporated.

Place the dough in a greased bowl, cover with plastic wrap or a damp towel, and let rise in a warm place until doubled in size (about 1-2 hours).

In a medium bowl, beat together softened butter and sugar until light and fluffy (2-3 minutes). Add almond flour, flour, an egg, egg yolk, almond extract, vanilla extract, and salt. Mix until smooth and creamy. Fold in all-purpose flour and sliced almonds. Set aside.

Grease a 9x13-inch baking pan with butter. Turn the chilled dough out onto a lightly floured surface. Roll into a 16x12-inch rectangle, with the long edge facing you. Spread the frangipane filling evenly over the entire surface of the dough in a thin layer, leaving a ½-inch border at the far long edge. Sprinkle the orange-cardamom spice mix evenly over the frangipane. Sprinkle 2 tablespoons pearl sugar evenly over the filling.

Using a pizza cutter or sharp knife, cut the rectangle into 12 strips (each about 1 ⅓ inches wide). Starting from one short end, roll each strip individually into a spiral. Pinch the end to seal. Arrange the rolls cut-side up in your prepared baking pan, spacing them slightly apart.

Cover loosely with plastic wrap or a clean kitchen towel and let rise in a warm place for 45-60 minutes, until puffy and almost doubled in size.

Preheat oven to 325°F. Bake for 27-30 minutes, or until the rolls are golden brown on top and the centers register about 200-205°F on an instant-read thermometer inserted into the very center of a roll. Let rest in the pan for 10 minutes after baking.

While rolls are baking, whisk together melted (and slightly cooled) butter, powdered sugar, almond extract, vanilla extract, pinch of salt, and 2 tablespoons milk or cream. After the rolls have rested for 10 minutes and are still warm, drizzle the almond glaze generously over the top. Immediately sprinkle the toasted sliced almonds over the glaze so they stick. Let the glaze set for 10-15 minutes before serving.