In the bowl of stand mixer, combine 2 cups of flour and the yeast with a fork.
In a small saucepan over medium heat, warm milk, sugar, 1/3 cup of butter, and salt until it reaches 115-120 degrees, stirring occasionally. Add this to the bowl of flour. Using the dough hook attachment, mix it on low speed for 15-20 seconds.
Add the 2 eggs. Beat on low for 30 seconds, scrape down the sides, then beat on medium for about 3 minutes.
Add the remaining 2 cups of flour, 1 cup at time. Beat just until each cup is incorporated and scrape down the sides in between. The dough should pull away from the sides of the bowl, but still be a little sticky.
Dust a work surface with the remaining 2 Tbsp of flour and turn your dough out. Knead by hand for 3 to 5 minutes, incorporating all the flour.
Shape it into a ball and place it in a lightly greased bowl. Turn it over once to coat, cover with a tea towel and allow to rise until doubled in size; about 30 minutes.
Meanwhile, make the filling. Place chopped, pressed cherries in a small saucepan. Combine the corn starch with 2 tbsp of reserved cherry juice to make a slurry. Add this to the saucepan along with the sugar, lemon zest + 1 tsp of lemon juice. Cook them over medium-low for up to 5 minutes. Stir often to prevent burning. Take it off the heat as soon as it thickens. Taste and add more lemon juice if needed. Set aside to cool.
Lightly dust a work surface and rolling pin with flour. Punch down the dough and turn it out on your work surface. Roll the dough into a rectangle approximately 12" x 18".
Spread the cherry filling all over. Starting with a long edge, roll the dough into a cylinder. Using a sharp knife, cut the dough into 12 equal rolls. Place the rolls into a lightly greased 9"x13" baking dish. Cover and allow to rest on the counter for another 45 minutes. They will expand and fill the pan.
Preheat the oven to 350 degrees during the last 20 minutes of rest time. Bake for 20 minutes. Check them for doneness. The dough around the edges of the pan may turn a very light golden brown. If they are still pale, bake them for up to 5 minutes longer. Remove them to a cooling rack.
Prepare the icing by combining what's left of the stick of butter with the cream cheese. Mash them together with a fork or back of a spoon until smooth. Add 1/2 cup of powdered sugar and mix. Add the vanilla, milk and remaining cup of confectioner's sugar. Mix until smooth.
Spread icing over the rolls with an offset spatula or spoon. Sprinkle almonds over the sweet rolls.