Season chicken pieces uniformly with salt, pepper, and dried oregano.
Heat 1 tablespoon of olive oil in a large heavy-bottomed skillet over medium-high heat until shimmering.
Add chicken to the skillet in a single layer and sear until an internal temperature of 165°F (74°C) is reached, approximately 6-8 minutes. Remove chicken and set aside.
Add the remaining 1 tablespoon of olive oil to the same skillet. Place Brussels sprouts cut-side down in the pan.
Sear Brussels sprouts undisturbed for 5 minutes until deep golden brown, then stir and cook for an additional 3 minutes.
Incorporate minced garlic and cook for 60 seconds until fragrant, ensuring the garlic does not burn.
Deglaze the pan with chicken broth and lemon juice, scraping the fond from the bottom of the skillet.
Return the chicken to the skillet and add the butter and lemon zest.
Toss the mixture continuously for 2 minutes until the butter is emulsified into a light sauce. Serve immediately.