While rice cooks, stir paprika and berbere seasoning into the onion mixture, adjusting to taste. Add chicken to the pot and brown, 5 to 7 minutes per side. Pour in tomatoes and stir to combine. Pour in enough chicken broth to thin mixture out to stew consistency. Reduce heat and let simmer until chicken is no longer pink in the center, 20 to 30 minutes, adding hard-boiled eggs when stew has about 10 minutes of cooking time left.