Combine white rice and chicken broth in a saucepan, bring to a boil, then reduce heat and simmer covered for 18 minutes until liquid is absorbed.
Heat olive oil in a large skillet over medium-high heat.
Add ground turkey to the skillet and cook, breaking it into small crumbles with a spatula, until fully browned and no longer pink.
Stir in the minced garlic, dried oregano, dried thyme, salt, and black pepper; cook for 2 minutes until fragrant.
Prepare the fresh vegetables by dicing the cucumber, halving the tomatoes, and slicing the red onion.
Assemble the bowls by portioning the cooked rice into four equal servings.
Top each rice portion with the cooked turkey mixture, cucumbers, tomatoes, red onions, and Kalamata olives.
Garnish each bowl with crumbled feta cheese and fresh parsley.
Serve immediately with a dollop of tzatziki sauce and a lemon wedge on the side.