Preheat oven to 350 degrees. Grease and flour a bundt pan and set aside.
Cream butter in a mixer or food processor until smooth a slightly lighter shade of yellow. Add eggs, brown sugar, granulated sugar, milk, and vanilla extract and continue mixing until uniform.
In another bowl, mix together flour and sea salt. Add wet mixture to flour mixture and stir by hand until batter is uniform and no dry pockets remain.
Divide batter evenly into two bowls and add melted chocolate and cocoa powder to one bowl. Mix until uniform in color.
Add peanut butter to the other bowl and mix until uniform in color.
Fill prepared bundt pan about halfway with batter by adding alternating spoonfuls of chocolate and peanut butter batters. Use a knife to swirls the batters together then repeat process with remaining batter until pan is full.
Place pan in oven and bake for about an hour or until a toothpick inserted into multiple parts of the cake comes out clean. Remove cake from oven and let it sit in pan for about 10 minutes then carefully invert it onto a plate to finish cooling.
While cake cools, prepare frosting: beat powdered sugar and butter together using a whisk attachment for about 30 seconds then add peanut butter and vanilla extract. Mixture will be somewhat coarse and crumbly.
Add in milk one tablespoon at a time until desired texture is reached then continue mixing for about three minutes or until frosting is uniform and fluffy. It should be glossy in appearance and thick enough that it doesn't run or easily drip off whisk when raised.
Spoon and spread frosting over top of pound cake and allow to fall down the sides. For an additional optional garnish, sift cocoa powder over top of cake.