In a medium-size, heavy-bottom saucepan, place the strawberries, sugar, salt and water, and mix to combine.
Place the strawberry mixture over medium heat and cook, stirring occasionally to prevent the mixture from burning, until the strawberries are softened and the liquid has reduced by about 1/4 (about 10 minutes).
Remove the saucepan from the heat and, using a stick blender, blend the mixture until smooth.
You can also allow the mixture to cool briefly and then place it in a blender or food processor and process until smooth.
Set the syrup aside to cool.
Make the cupcake batter.
Preheat your oven to 350°F. Grease or line the wells of a standard 12-cup muffin tin and set it aside.
In a small bowl, place the flour, xanthan gum, baking powder, baking soda, and salt, and whisk to combine well, then set the bowl aside.
In a large bowl with a hand mixer or the bowl of a stand mixer fitted with the paddle attachment, place the butter and sugar, and beat until light and fluffy.
Add the egg and egg white, and vanilla, and mix until well-combined. Add the completely optional red gel food coloring, and mix until well-combined.
Add about half of the dry ingredients, and mix until just combined. Add the strawberry syrup and milk, and mix. Add the remaining half of the dry ingredients, and mix until just combined.
Bake the cupcakes.
Fill the prepared wells of the muffin tin about 3/4 of the way full of the batter, and shake into an even layer.
Place the muffin tin in the center of the preheated oven and bake until a toothpick inserted in the center of the cupcakes comes out clean (about 19 minutes).
Remove from the oven and and allow to cool in the muffin tin for 10 minutes before transferring to a wire rack to cool completely. Repeat with the remaining batter.
Make the (optional) frosting.
In the bowl of your stand mixer or a large bowl with a handheld mixer, place the butter and beat on medium speed until light and fluffy (about 4 minutes).
Add 3 1/2 cups of the confectioners’ sugar and the salt, and beat on low speed until the sugar is absorbed by the butter. Add the strawberry syrup and beat to combine.
The frosting should be light and fluffy, and should hold its shape easily when scooped with a spoon. Add more confectioners’ sugar and/or milk by the half-teaspoonful as necessary to achieve the desired consistency.
Once the cupcakes have cooled, frost the cupcakes generously with the frosting, and top with a small dollop of the remaining strawberry syrup.
Make the (optional) strawberry glaze.
Place the confectioners’ sugar in a small bowl, and add about 1 tablespoon of the strawberry syrup. Mix until it resembles a very thick paste.
Add more syrup by the half teaspoon as necessary to create that thick paste. It should be difficult to stir.
Add water by the literal drop, and mix completely, until the glaze is thickly pourable. Dip the top of each cooled cupcake, still in its liner, into the top of the glaze, bobbing the cupcake up and down a couple of times in the glaze.
Slowly raise the cupcake, still upside down, from the glaze to break the trail of glaze, then turn it over and place the cupcake down, right side up. Allow to set at room temperature.