Preheat the oven to 350 degrees F. Butter a 9-by-13-inch baking pan.
In a medium-large saucepan over low heat, melt the butter with the unsweetened chocolate, whisking occasionally, until smooth and fully melted. Sprinkle in cocoa powder and whisk to combine. Remove the pan from heat and allow to cool for about 5 minutes.
Stir in sugar and vanilla until just combined. Stir in the eggs, one at a time. Gently stir in the flour until halfway incorporated. Add the white chocolate chips and stir just until combined.
Pour the batter (it will be very thick!) into the baking pan and spread to even out the top.
Bake 20 to 25 minutes, then check the brownies with a toothpick; if they are overly gooey/messy, return them to the oven for another 5 to 10 minutes. (Just be careful not to burn the edges.)
Allow the brownies to cool completely. Cut into 1-by-2-inch fingers and place on a rack over a baking sheet.
Melt the almond bark in a double-boiler (or in the microwave in 30-second intervals). Dip one end of each brownie finger into the almond bark and then return to the rack until the coating has hardened, 5 to 10 minutes.