Season chicken pieces evenly with salt, pepper, and dried oregano.
Heat 1 tablespoon of olive oil in a large heavy-bottomed skillet over medium-high heat.
Add chicken to the skillet and sear until golden brown and cooked through, approximately 6 to 8 minutes. Remove chicken from the pan and set aside.
Add the remaining tablespoon of olive oil and the Brussels sprouts to the same skillet, cut-side down.
Cook Brussels sprouts undisturbed for 5 minutes to achieve a char, then stir and cook for an additional 3 to 5 minutes until tender.
Reduce heat to medium and add the butter and minced garlic. Sauté for 60 seconds until the butter is melted and garlic is fragrant.
Stir in the lemon juice, lemon zest, and red pepper flakes, scraping the bottom of the pan to release any browned bits.
Return the chicken to the skillet and toss thoroughly to coat everything in the lemon garlic butter sauce.
Garnish with additional lemon zest if desired and serve immediately.