Preheat oven to 350 degrees F.
To make the rhubarb compote: In a small saucepan over medium heat, bring rhubarb, water and sugar to a boil. When sugar is dissolved, lower heat to a simmer and cook until rhubarb is soft, about 10 minutes. Remove from heat and cool slightly. Puree in a blender until smooth, if necessary. The rhubarb should break down to a smooth compote.
To make the brownie batter: In a medium bowl, sift together flour, baking powder, Chile powder, cinnamon and salt. Set aside. In a clean microwavable glass bowl, melt bittersweet and unsweetened chocolate together in the microwave at 50 percent power or in a double boiler. Set aside.
In a stand mixer, cream butter and sugar on medium speed. Add the eggs, 1 at a time, combining well. Add in the vanilla and rum. Stir the rhubarb into the chocolate mixture, then add to the batter. Mix until combined. Add the flour mixture and mix just until incorporated. Scrape down the sides with a rubber spatula and gently fold in the semisweet chocolate and walnuts. Do not over mix. Spray an 8 by 8 by 2-inch clear glass baking dish with shortening spray. Line bottom with parchment paper, then spray parchment. Pour batter into the prepared pan and smooth out top. Bake until a toothpick inserted in the center comes out clean, about 35 to 40 minutes. Remove from the oven and set aside to cool. Cut into squares and serve.