Place milk in a microwave safe measuring cup. Heat for 30-45 seconds in the microwave, until it’s about 120°F (use a thermometer if you have one or think hot bathwater when feeling it. Add yeast and 1/2 teaspoon of sugar and stir. Let it sit for a few minutes to proof.
Place 1/3 cup sugar, butter, salt, and egg in the bowl of a stand mixer fitted with the paddle attachment. Mix until the butter is distributed throughout the liquids, although it may be chunky. Pour in the milk/yeast mixture and stir for a few seconds.
Add flour and stir with the paddle attachment just until the mixture starts to stick to the paddle. Then replace the paddle with the dough hook. Continue mixing on low speed until the dough forms a ball in the center of the bowl. The dough should be in one piece and it will be slightly sticky, but you should be able to handle it without getting too much dough on your fingers. If it’s really wet, add up to 1/2 cup more flour (but add it 1/4 cup at a time). I always use 3 cups, but depending on the temperature in your kitchen and where you live, you may need a little more.
Spray a large bowl with cooking spray and place the dough ball in it. Spray the top of the dough ball with cooking spray (lightly) and cover the bowl with plastic wrap. Let sit for 1-2 hours until it doubles in size.
Note on rising: if your house is warm, it should rise no problem. If it’s cold in your house, it may take longer for the dough to rise, so plan accordingly!
Make the filling: place almond paste, egg, and sugar in a food processor and process until smooth and creamy and no lumps of almond paste remain. If you don’t have a food processor, I suggest cutting or breaking the almond past into small chunks and then using a mixer to incorporate the sugar and egg. A food processor is easier (and faster!)
When the dough has risen, turn it out onto a cutting board that has been lightly dusted with flour. Roll it into a rectangle that’s about 10x14”. Spread the filling on the dough and tightly roll it up. Using a serrated knife, cut the dough into 9 large cinnamon rolls or 12 smaller. For 9 rolls, use a 9” square pan. For 12 rolls, use a 9x13” pan. Spray your pan with cooking spray and place the rolls gently in the pan.
You have two options now. 1. Let the dough rise for 30 minutes, then bake as directed below or 2. Cover with plastic wrap and refrigerate overnight, then remove the rolls from the refrigerator and let come to room temperature in the morning while the oven is preheating.
Preheat oven to 350°F. Bake rolls for 25-35 minutes, until they’re golden brown on the top. Let cool at least 15 minutes before frosting and serving.
Make frosting: whisk melted butter, powdered sugar, and almond extract until smooth. Add 1 tablespoon of milk and whisk until smooth. If the glaze is too thick for your liking, you can add up to 1 more tablespoon of milk. (The pictured rolls use 1 tablespoon.) Garnish with sliced almonds.