Combine the brown sugar, milk, salt, butter, peanut butter, and cocoa in a large saucepan over medium-high heat. Stir to dissolve as the mixture heats. Continue to cook, stirring, until the mixture begins to bubble around the edges of the pan and reaches 234 degrees to 240 degrees F on a candy thermometer, or the soft ball stage (that is, when a bit of the mixture is dropped into cold water, it forms a soft ball that flattens), about 12 minutes. Remove from the heat and stir in the pecans. Drop the mixture by the tablespoonful onto a waxed or parchment paper on a baking sheet and let cool completely. Lift the pralines off the paper with a thin knife. Pralines can be stored in an airtight container at room temperature for up to 2 weeks.
In a medium-size, nonreactive saucepan over medium heat, combine the milk, cream, sugar, and vanilla bean and pulp. Whisk to dissolve as the mixture heats. Heat the mixture to the scalding point (when bubbles form around the edges of the pan); do not let it boil. Remove from the heat. Beat the egg yolks in a large mixing bowl. Add the hot cream mixture about 1/4 cup at a time to the beaten yolks, whisking well after each addition. Pour the mixture back into the saucepan and cook, stirring over medium heat until the mixture becomes thick enough to lightly coat the back of a spoon, 2 to 3 minutes, do not let it boil. Remove from the heat and strain through a fine-mesh strainer into a glass bowl. Cover the top of the mixture with plastic wrap (this will keep a skin from forming) and let cool. Place the mixture in the refrigerator and chill completely. Pour the mixture into an ice cream machine and follow the manufacturer's instructions for the churning time. Once the ice cream is almost ready, about 5 minutes before the churning time is complete, add the crumbled pralines through the ingredients spout. Continue to churn until the ice cream freezes. Line an 8 1/2 by 4 1/2 by 2 1/2-inch loaf pan with plastic wrap. Scoop the ice cream into the pan, smooth the top, cover, and freeze until firm, about 4 hours. When ready to assemble the ice cream sandwiches, lift the ice cream out with the plastic wrap.
Preheat the oven to 350 degrees F. Butter and flour a 9 by 5 by 3-inch loaf pan with 1/2 teaspoon of the butter and 1/2 teaspoon of the flour. In a large mixing bowl, cream the remaining 1/2 pound (2 sticks) butter and the sugar together with an electric mixer until smooth. Add the eggs 1 at a time, beating after each addition. Beat in the vanilla. Into a medium-size mixing bowl, sift the remaining 1 1/2 cups flour, the cocoa, baking powder, and salt together. Add 1/3 of the flour mixture at a time to the butter/sugar mixture, beating after each addition. Spoon the batter into the prepared pan and bake until it springs back when touched, about 50 minutes. Remove from the oven and let cool in the pan on a wire rack for 10 minutes, then remove it from the pan and let cool completely on the rack. After the ice cream is firm, remove it from the pan. Cut the ice cream into 16 slices. Place 1 slice of ice cream between 2 slices of pound cake, forming a sandwich. Repeat the process until all of the cake is used. Wrap each sandwich in plastic wrap and freeze until ready to serve. To serve, unwrap the sandwiches and serve each with a praline on the side.