In the bowl of a stand mixer fitted with the paddle attachment, combine 2 cups of flour, sugar, yeast, and salt. Mix on low until well blended.

In a microwave-safe bowl, heat the milk and butter until warm to the touch (about 110-115°F) and the butter is mostly melted, roughly 45 seconds. Do not let it steam or get too hot, as that can kill the yeast.

Pour the warm milk mixture into the flour mixture. Add the egg, almond extract, and vanilla extract. Beat on low until combined, then increase to high and beat for 2 minutes. The dough will be very soft and batter-like; this is correct and helps develop gluten.

Switch to the dough hook. Add 1 1/2 cups of flour and knead on low until incorporated. Scrape down the sides of the bowl. Add the remaining 1 cup of flour (for a total of 4 1/2 cups) and knead on low, stopping occasionally to redistribute the dough, until it pulls away from the sides and forms a ball around the hook.

Increase speed to medium-low and knead for about 10 minutes, until the dough is smooth and supple. To test, stretch a quarter-sized piece of dough; you should be able to see light through it without it tearing. If it tears, knead a few minutes more.

Place the dough in a lightly oiled bowl, cover with plastic wrap or a clean dish towel, and let rise in a warm spot for 1 hour, or until doubled in size.

In a medium bowl, combine the softened butter, almond meal, sugar, egg, almond extract, vanilla extract, and salt. Stir until a thick, smooth paste forms. Set aside.

Turn the risen dough out onto a well-floured surface. Roll it into a 12-inch by 18-inch rectangle, with the longer side facing you.

Using an offset spatula, spread the almond filling evenly over the entire surface of the dough, all the way to the edges.

Starting from the long end farthest from you, roll the dough tightly toward you into a log. Pinch the seam to seal.

Using unflavored dental floss or a very sharp knife, cut the log into 12 equal rolls. Arrange them in a 9x13-inch baking pan lined with parchment paper. Cover loosely with a dish towel and let rise for another hour, until doubled and puffy.

Preheat the oven to 350°F. Bake the rolls for about 30 minutes, until golden brown all over. Transfer the pan to a wire rack to cool slightly.

In the bowl of a stand mixer fitted with the paddle attachment, beat together the butter, cream cheese, powdered sugar, vanilla extract, almond extract, and salt. Start on low, then increase to high until smooth and fluffy. Spread the frosting over the warm rolls and sprinkle with slivered almonds. Serve warm.