Heat a large skillet or medium saucepan over medium-high heat.
Add the oil and butter to the hot pan. When the butter melts, add the diced onion and cook, stirring occasionally, until the onion is soft and lightly golden, about 3–4 minutes.
Stir in the minced ginger and garlic and cook for about 30 seconds, stirring so they do not burn.
Add the chicken pieces, tomato paste (or tomato sauce), garam masala, chili powder (or paprika), fenugreek, cumin, salt, and black pepper. Stir to combine and cook until the chicken is cooked through, about 5–6 minutes.
Pour in the heavy cream, reduce heat to medium-low, and simmer gently, stirring occasionally, until the sauce thickens slightly and flavors meld, about 8–10 minutes.
Serve the butter chicken over hot cooked rice with naan on the side.