Pat the chicken breasts dry with paper towels. Season both sides with salt, black pepper, and paprika.
Heat the olive oil in a large skillet over medium-high heat until shimmering.
Add the chicken breasts to the skillet and cook for 6 to 7 minutes on one side without moving them, until golden brown.
Flip the chicken breasts and cook for another 5 to 6 minutes, or until the internal temperature reaches 165°F (74°C). Remove the chicken from the skillet and set aside on a plate to rest.
Reduce the heat to medium. In the same skillet, add the butter and minced garlic. Sauté the garlic for about 30 seconds until fragrant, stirring constantly to prevent burning.
Add the chopped kale to the skillet and stir to coat with the garlic butter.
Pour in the chicken broth and cover the skillet. Let the kale steam for 3 to 4 minutes until wilted and tender.
Remove the lid and stir the kale. Cook for an additional 1 to 2 minutes to allow any excess liquid to evaporate.
Slice the rested chicken breasts and serve them alongside the garlic kale.