Preheat your oven to 350 degrees. Fill two muffin tins with paper liners and butter the tops of the muffin tin to prevent sticking.
In a large mixing bowl, whisk together flour, sugar, cocoa powder, baking powder, baking soda, and salt until well combined.
Add in the eggs, sour cream, applesauce, melted butter, buttermilk, molasses, and vanilla extract. Mix until everything is blended smoothly.
Stir in the hot water and mix with an electric mixer on medium speed for 2 minutes until the batter is smooth and velvety.
Pour about 1/4 cup of the mixture into each of the 24 lined muffin cups, filling them about 3/4 full. There should be a little batter left over, so no worries!
Bake in the preheated oven for 17 to 18 minutes. Check with a toothpick; it should come out with a few moist crumbs attached.
Once baked, allow the cupcakes to cool completely before frosting.
For the frosting, melt butter in a medium saucepan over medium heat. Whisk in brown sugar and salt, bringing the mixture just to a boil.
Reduce the heat and let it simmer for 2 minutes, stirring constantly to avoid burning.
Stir in half-and-half and bring the mixture just to a boil again, stirring consistently.
Remove the mixture from heat and stir in vanilla extract. Let it cool to warm.
Once cooled, beat in powdered sugar until smooth. Add hot water as needed to thin out the frosting, about 1 tablespoon at a time.
Immediately spread the frosting over the cooled cupcakes before it sets. Enjoy your delicious treats!