Preheat the oven to 450F or 425F convection (use convection if you can). Line a rimmed baking sheet with parchment paper.
Add the potatoes to half of the baking sheet and tomatoes to the other half. Drizzle potatoes with 2 tbsp olive oil and ¾ tsp salt and the tomatoes with 1 tablespoon olive oil and ¼ teaspoon salt. Toss each separately to coat. Bake for 20 minutes, or until potatoes are browned in spots and cooked through and tomatoes have burst open and slightly charred on top.
Add all turkey patty ingredients to a medium bowl and use your hands to mix thoroughly. Form into small patties (I used a small cookie scoop, but you can also just use a heaping tablespoon).
Line a large plate or baking sheet with paper towel. In a large skillet over medium-high heat, add about 1 tablespoon oil. Once the oil is hot and shimmering, add patties to the pan and press down gently. Cook for 2-3 minutes on each side, or until browned and cooked through. Transfer the patties to the prepared plate or baking sheet. Wipe out the skillet and repeat with remaining patties.
Make the tzatziki sauce by mixing together the yogurt, cucumber, lemon juice, salt and pepper.
Add potatoes, kale, and olives to a large bowl and toss with vinegar, remaining 1 tablespoon oil, and pepper.
Serve patties with the warm roasted potatoes salad, burst tomatoes, and tzatziki sauce. Top with toasted nuts and chopped dill or parsley.