At least one hour or as early as one day before you are serving, prepare the salsa and tzatziki. For the cucumber salsa, toss the olive oil, vinegar, tomatoes, cucumbers and onions in a bowl and season with salt and black pepper as needed. 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. Again, 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. Cook the ground lamb or turkey with the salt, pepper, onion and garlic, breaking up the meat into small pieces and cooking until the meat is cooked through, 8-10 minutes.
Drain any 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.
Warm the pita breads in a cast iron skillet or in the microwave until soft and heated through. Serve the tacos by spooning meat into the center of a pita bread and topping with cucumber salsa and tzatziki.
Notes
Pita Bread: here is my favorite homemade version. Make Ahead: the cucumber salsa and the tzatziki sauce can be prepared up to a day in advance and refrigerated. Crockpot: Sally mentions that she's made the meat mixture and kept it on low in a crockpot for up to 4 hours to let the flavors develop (and help when entertaining or if you need some flexibility).