Cut the chicken into chunky cubes, around 1½ to 2 inches / 4 to 5 cm.
Place the olive oil, milk, tomato paste, Turkish red pepper paste, chili flakes, paprika, black pepper, salt, and garlic, if using, in a large bowl. Whisk until combined.
Add the chicken pieces and mix well until every piece is coated with the marinade.
Cover the bowl and refrigerate for at least 2 hours, or preferably overnight.
When ready to cook, peel the onion and cut it into chunky pieces similar in size to the chicken.
Cut the tomatoes into wedges, or use whole cherry tomatoes.
Cut the Turkish green chilies into large pieces. If using bell pepper, cut it into chunky squares.
Thread the chicken pieces onto metal skewers. Add the vegetables between the chicken pieces, or thread them onto separate skewers.
To cook on the BBQ, heat the grill until hot and cook the skewers for 12 to 14 minutes, turning a few times, until lightly charred and cooked through.
To cook in the oven, preheat the oven broiler to 410°F / 210°C. Place the skewers on an aluminum foil-lined baking sheet and cook for about 15 minutes, turning once.
The chicken is ready when the thickest piece reaches 165°F / 74°C in the center. Let the chicken rest for a few minutes before serving.