Peel the onions and garlic. Cut the bell pepper, onions, and garlic into large pieces. Cut open the burger buns and set aside.
Wash the chicken breast and pat it dry. Remove any visible tendons. Cut the meat into large pieces.
Pass the chicken pieces through a meat grinder together with the onions, peppers, and garlic to create a combined ground mixture.
Add salt, pepper, hot paprika powder, and sweet paprika powder to the ground chicken mixture. Mix thoroughly by hand until evenly combined.
Heat the rapeseed oil in a large pan over medium-high heat. Toast the inside surfaces of the burger buns for 1-2 minutes until lightly golden. Transfer to a plate and top each bun with 2 slices of cheese.
In the same pan over medium heat, cook the seasoned ground chicken mixture for 4-5 minutes, stirring frequently and breaking it apart. The chicken is done when there is no pink remaining and the internal temperature reaches 74 °C (165 °F) if measured.
Stir in the tomato paste and cook for 1 minute while stirring. Pour in the water to deglaze the pan. Add ketchup to taste and adjust seasonings as needed.
Spread the chicken mixture on the bottom half of each bun with cheese. Close the buns and serve immediately with napkins.