In a large mixing bowl, whisk together 1 ⅓ cup of the brown sugar, flour, cocoa powder, instant coffee, baking soda, baking powder, and salt. Set aside.
 
Heat skillet over medium heat. Add pecans and dry toast for a few minutes until they start to smell fragrant, 3 to 4 minutes. Be careful not to burn. Add the butter and let it melt. Stir in the remaining 1 cup of brown sugar. Stir and continue to cook while the sugar starts to bubble and melt, 3 to 4 minutes. Carefully add 1 cup of coconut milk and stir to combine. Continue to cook up to 5 minutes, while stirring, until the sugar is completely melted and a silky, amber caramel has been formed. Remove from heat. Spoon out about 1/2 cup of the pecan caramel and reserve for serving. Spread the remaining caramel evenly over the bottom of the skillet.
 
Preheat the oven to 325ºF. In a small pot, heat the remaining 1 ½ cups of coconut milk. Bring to a simmer then remove from heat and add the chocolate chips and vanilla. Gently stir until the chips are melted.
 
Place the black beans in a food processor. Add the melted chocolate chips. Purée for a minute or more until the mixture tastes smooth. Pour this mixture into the bowl with the dry ingredients. Stir until combined. 
 
Gently pour the batter from the bowl into the skillet over the pecan caramel. Place the skillet in the oven and bake for 25 to 30 minutes. When done, the brownie should be slightly crisp around the edges and pulling away from the sides of the pan. The center should be dark and a little bit moist. Don't overbake. Set aside to cool for about 10 minutes.
 
To serve, use a large serving spoon to scoop the brownies onto individual plates. Add a scoop of vanilla ice cream and top with a spoonful of pecan caramel sauce. Alternatively, place scoops of ice cream on the brownie while still in the skillet and drizzle pecan caramel over everything. Pass the spoons around and have everyone dig in.