Preheat the oven to 475°F.
In a large bowl, combine the chicken, garlic, olives, feta, spinach, eggs, panko, salt, and pepper with your hands. Form into 4 patties on a baking sheet.
Bake for 20-25 minutes, or until cooked through or the internal temperature reaches 160°F.
Make the vinaigrette by combining all of the ingredients except the oil in a bowl with a whisk. Continue whisking while you drizzle in the oil until emulsified. Adjust seasoning with salt and pepper. Toss with the romaine in a large bowl.
To make the relish, combine all the ingredients in a bowl.
To make the cucumber yogurt, combine all the ingredients except the cucumber in a small bowl. Whisk well to combine. Fold in cucumber and season to taste.
Serve the chicken burgers on brioche rolls topped with romaine salad, Greek relish and cucumber mint yogurt.