In a blender jar, combine the onions, garlic, and ½ cup water. Process on high speed for 1 minute, or until smooth.
In a small saucepan over low heat, combine the crumbled beef, 2 cups water, and the processed onion and garlic. Simmer, uncovered, for 30 minutes. Using a large spoon, skim the frothy substance that rises to the surface; discard. Repeat 2 or 3 times during the cooking time. Also use the spoon to break up clumps of meat for a smooth consistency. Set aside off the heat.
In a large skillet over medium heat, heat the oil until it shimmers. Lower the heat. Stirring continuously, add the flour and cook until the flour turns a light golden color. Set aside off the heat.
In a medium saucepan over low heat, heat the broth and 1 cup water until steaming hot, almost boiling. Meanwhile, in a small bowl or container with a lid, combine the chili powder, salt, Holy Trinity, and cayenne pepper, whisking or shaking to blend. Stir the combined spices into the hot broth mixture, blending until smooth.
Gradually add the cooked beef and chili powder–broth mixture to the cooked flour, stirring constantly to remove lumps. Stir and cook over low heat for 5 minutes, or until the mixture is almost as thick as ketchup.
Set aside off the heat for at least 10 minutes to let the flavors mellow before serving.
The sauce may be refrigerated for up to 1 week or frozen for up to 3 months.