Place the eggs in a small saucepan and cover with water by about 1 inch. Bring to a high simmer over medium-high heat and cook for 1 minute. Cover, remove from the heat and let sit 12 minutes. Drain the eggs and rinse under cold water, then peel and thinly slice.
Meanwhile, cook the veggie burgers as the label directs. Whisk the yogurt, garlic, paprika, 2 tablespoons water, and salt to taste in a small bowl. In a large bowl, toss the arugula, roasted red peppers, cucumber, olive oil, mint, feta, and salt to taste.
Cut 1 inch off the top of each pita to make an opening; stuff the pita strip inside the pita to reinforce the bottom. Stuff each pita with a veggie burger, some arugula salad and a few slices of hard-boiled egg. Drizzle with the yogurt dressing. Serve with pickles.