Season chicken with salt, pepper, and 1 1/2 tablespoons paprika. In a large skillet over medium-high heat, heat 1 tablespoon olive oil. Sear chicken skin-side down until golden, about 6 to 8 minutes. Flip and cook 3 minutes more, then transfer to a plate skin-side up; set aside.

Return pan to heat and heat remaining oil. Add garlic and cook until fragrant, 1 minute. Add peppers and cook until slightly tender, 4 to 6 minutes. Season with salt, pepper, and remaining paprika. Add rice, chicken broth and heavy cream and bring to a simmer. Return chicken to skillet and cover. Simmer until rice is tender and chicken is cooked through, about 20 minutes.

Fold in spinach until wilted and serve.