Cut the chicken into small, even bite-size pieces, then season with salt and black pepper. Let it sit for a few minutes while you prepare the remaining ingredients.
Toss the chicken with 1 tablespoon of the flour and shake off any excess.
Heat the olive oil in a large skillet over medium-high heat. Add the chicken in a single layer and cook until golden and cooked through. Work in batches if needed, then transfer the chicken to a plate.
Reduce the heat to medium-low and melt the butter in the same skillet.
Add the minced garlic and cook for about 30 seconds, just until fragrant.
Stir in the remaining 1 tablespoon flour and the oregano.
Slowly pour in the water or chicken broth, stirring until smooth. Let the sauce simmer gently until slightly thickened.
Return the chicken and any juices from the plate to the skillet. Toss gently until every piece is coated in the garlic butter sauce, then cook for about 1 minute, just until heated through.
Remove from the heat, sprinkle with fresh parsley, and serve immediately.