Position a rack in the upper third of the oven and preheat to 400 degrees F. Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add the onion and bell pepper and cook, stirring occasionally, until golden, 6 to 8 minutes. Add the tomato paste and cook, stirring, until brick red, 1 minute. Add the beef, 2 tablespoons water, 3/4 teaspoon salt, and pepper to taste and cook, breaking up the meat, until browned, 3 to 4 minutes. Remove from the heat and stir in 1/4 cup yogurt and 2 teaspoons vinegar. Season with salt and pepper and transfer to a bowl. Wipe out the skillet and return to medium heat. Brush the pitas with 1 tablespoon olive oil, then lightly toast in the skillet, about 45 seconds per side. Arrange the pitas on a baking sheet and top evenly with the beef mixture. Transfer to the oven and bake 6 minutes. Whisk the remaining 1/4 cup yogurt, 1 tablespoon each olive oil and vinegar, and salt and pepper to taste in a bowl. Add the lettuce, beets and cucumber and toss. Slice the pizzas and serve with the salad.