Step 1: Preheat your oven to 350°F (175°C). Line a cupcake pan with cupcake liners and set aside.
Step 2: In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, cocoa powder, baking soda, baking powder, and salt until well combined.
Step 3: In another bowl, whisk together the eggs, sour cream, applesauce, melted butter, buttermilk, molasses, and vanilla extract until smooth.
Step 4: Pour the wet ingredients into the dry ingredients and stir until just combined. Be careful not to overmix.
Step 5: Carefully stir in the hot water until the batter is smooth and well blended. The batter will be thin, but that’s okay!
Step 6: Using a ladle or a measuring cup, fill each cupcake liner about two-thirds full with batter.
Step 7: Bake in the preheated oven for 18-20 minutes, or until a toothpick inserted into the center of a cupcake comes out clean.
Step 8: Remove the cupcakes from the oven and let them cool in the pan for 5 minutes before transferring them to a cooling rack to cool completely.
Step 9: In a medium saucepan over medium heat, melt the butter. Stir in the dark brown sugar and half-and-half, and bring to a gentle boil. Let it boil for 2-3 minutes, stirring constantly. Remove from heat.
Step 10: Add a pinch of salt and the vanilla extract to the mixture. Let it cool slightly.
Step 11: Gradually whisk in the powdered sugar until the frosting is smooth and creamy. If the frosting is too thick, add 1-2 tablespoons of hot water until you reach your desired consistency.
Step 12: Once the cupcakes are completely cooled, use a piping bag or a spatula to generously frost each cupcake with the penuche frosting.
Step 13: Serve your chocolate cupcakes with penuche frosting to friends and family, and watch them disappear in no time!