Season chicken thighs well with ½ teaspoon salt (add more to taste), pepper, and garlic granules. In a large heavy-bottomed pot, heat oil over medium-high heat. Once oil is hot, add chicken thighs skin-side down and cook undisturbed until nicely browned, about 5–6 minutes. Flip and brown the other side, about 4–5 minutes more. Transfer to plate and set aside.
Pour the fat oil from the pot (but keep all the brown bits). Add tomato sauce and stir until pot has been deglazed. Add mole paste and stir until dissolved, about 2–3 minutes. Add broth and season with remaining salt and sugar. Stir until the mole sauce has thickened, about 5–7 more minutes. Add back in the chicken and bring to a slow simmer. Cover and allow the chicken to finish cooking through, about 15 minutes more. Taste and adjust seasoning.
Garnish with chopped parsley and serve with rice on the side, if desired.
You will have some mole left over. Freeze leftover mole sauce for up to three months or seven days in your freezer.