Preheat your oven to 350°F (175°C). Line a muffin tin with cupcake liners to prevent sticking and make for an easy cleanup later.
In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, cocoa powder, baking soda, baking powder, and salt until well combined.
In another bowl, whisk together the eggs, sour cream, applesauce, melted butter, buttermilk, molasses, and vanilla extract. Make sure everything is mixed thoroughly.
Pour the wet ingredients into the bowl of dry ingredients. Stir with a rubber spatula until just combined. Be careful not to overmix!
Slowly stir in the hot water until the batter is smooth. It will be quite thin, but that’s what makes the cupcakes tender.
Using a measuring cup or ice cream scoop, fill each cupcake liner about two-thirds full with batter.
Bake in the preheated oven for 18-20 minutes, or until a toothpick inserted into the center comes out clean.
Remove the muffins from the oven and let them cool in the pan for 5 minutes before transferring them to a cooling rack to cool completely.
In a medium saucepan, melt the butter over medium heat. Stir in the dark brown sugar and cook for 2-3 minutes, stirring constantly.
Remove the saucepan from heat and whisk in the half-and-half and a pinch of salt until combined. Let it cool slightly.
Transfer the mixture to a mixing bowl. Add the vanilla extract and powdered sugar gradually, mixing until smooth. If the frosting is too thick, add 1-2 tablespoons of hot water to reach your desired consistency.
Once the cupcakes are completely cool, generously frost them with the penuche frosting. You can use a knife or a piping bag for a decorative touch.
