Heat oil in large skillet and stir in butter to melt. Season chicken thighs with salt and pepper. Cook thighs skin side down until golden brown. Flip chicken and continue to cook until golden brown. Remove chicken to a plate.
Stir in onions and cook until tender. Stir in curry, cayenne, cinnamon and cumin and cook until aromas are released. Stir in carrots and toss to coat. Add chicken stock and bring to a simmer.
Place chicken thighs back into skillet and stir in broccoli. Cover and simmer for 15 minutes to cook chicken.
Stir in cream and peas. Season to taste. Serve with basmati rice.