Heat 2 tablespoons of olive oil in a large non-stick skillet over medium-high heat. Add the ground chicken, onion, garlic, and diced green bell pepper. Cook until the chicken is no longer pink, breaking it up with a spatula, for about 5-7 minutes.
Reduce the heat to medium and add the ketchup, Worcestershire sauce, yellow mustard, tomato paste, and chili powder directly into the skillet. Stir well to ensure the chicken and vegetables are evenly coated.
Pour in the water and stir, ensuring everything in the skillet is well combined.
Reduce the heat to low and let it simmer for about 10-15 minutes, stirring occasionally, until the flavors have melded together and the sauce has thickened slightly.
While the chicken mixture is simmering, toast the brioche buns in the oven or on a griddle with a little bit of butter until lightly golden.
Once everything is ready, divide the sloppy joe mixture onto the bottom halves of the toasted brioche buns, then cover with the top halves.
Serve immediately with a side of your choice.