Pat the chicken breasts dry with paper towels. Season both sides evenly with kosher salt, black pepper, and garlic powder.
Heat 1 tablespoon of 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 an additional 6 to 7 minutes, or until the internal temperature reaches 165°F (75°C). Remove the chicken from the skillet and set aside to rest.
In the same skillet, add the remaining 1 tablespoon of olive oil and reduce heat to medium.
Add the minced garlic and sauté for 30 seconds until fragrant, being careful not to burn it.
Add the chopped kale to the skillet and stir to combine with the garlic and oil.
Pour in the chicken broth, cover the skillet, and cook for 4 to 5 minutes, stirring occasionally, until the kale is wilted and tender.
Remove the lid, stir in the lemon juice, and cook for another 1 minute to allow excess liquid to evaporate.
Slice the rested chicken breasts and serve alongside the sautéed kale.