In the bowl of a stand mixer, beat the egg whites with granulated sugar until the mixture begins to form stiff peaks.
Add peach food coloring (or two drops of red coloring and one drop of yellow) to the meringue. Mix only until the color is distributed.
Using a fine mesh sieve or flour sifter, sift the powdered sugar and almond flour to get rid of any lumps.
Carefully fold the dry ingredients into the meringue. Be extra cautious not to overmix the batter.
Place a plastic bag with the tip cut off or a pastry bag into a cup to hold it upright. Transfer the batter into the bag, remove the bag from the cup, and twist the bottom to secure the batter inside.
Line a baking sheet with parchment paper. Carefully pipe equal-sized circles onto the baking sheet, making them fairly thick. Tap the baking sheet 3-4 times on each side to remove any air bubbles and prevent your shells from cracking. Allow the macarons to sit at room temperature for 20 minutes, or until they create a bit of a hard outer shell.
Depending on the strength of your oven, bake the macaron shells at 300°F for 13-20 minutes. You'll know they're ready to be removed from the oven when you can easily lift them off the baking sheet. Avoid over baking the shells, as they will turn out dry.
Whisk the softened butter with the dulce de leche until well-combined.
Place another plastic bag with the tip cut off or pastry bag into a cup to hold it upright. Fill the bag with the butter and dulce de leche filling.
Pipe the dulce de leche filling onto one of the macaroon shells and immediately top it with another shell to create a sandwich. Repeat until you run out of shells and batter.
Store the macarons in an airtight container in the refrigerator until you're ready to serve them. They will stay fresh for up to a week. If you wish to prepare them in advance, the cookie shells can be made up to two weeks in advance so long as they are stored in an airtight container in the fridge.