For the cucumber salsa, in a medium bowl, add the tomatoes, cucumbers and onions. Add the olive oil, vinegar, salt and pepper and toss to combine. Cover and refrigerate for one hour or up to 24 hours to marry the flavors.
For the tzatziki, peel the cucumber and shred on the large holes of a box grater. Place the shredded cucumber in a clean kitchen towel and wring out the excess water until the cucumber is very dry.
In a medium bowl, stir together the strained cucumber, yogurt, feta, garlic and mint. Season with salt and pepper, to taste. The tzatziki can be refrigerated up to 24 hours. Give it a good stir before serving.
For the meat, heat a large, 12-inch nonstick skillet over medium heat. Add the ground meat, salt, pepper, onion and garlic. Cook, breaking the meat into small pieces, until the meat is cooked through, 8 to 10 minutes. Drain excess grease.
Stir in the oregano and tomato paste and cook over medium heat for 3-4 minutes, stirring often. Stir in the broth and let the mixture simmer for 5-10 minutes. Season with additional salt and pepper, to taste, if needed.
Warm the pita breads in a cast iron skillet or in the microwave until soft, warm and pliable. Spoon meat into the center of the pita breads and top with cucumber salsa and tzatziki.
Notes
Pita Bread: my favorite homemade recipe for flatbread is here. Make Ahead: the cucumber salsa and the tzatziki sauce can be prepared up to a day in advance and refrigerated.