For the yogurt sauce: Combine all ingredients in bowl; cover and refrigerate until ready to serve. (Sauce can be refrigerated for up to 4 days.)
For the burgers: Adjust oven rack to middle position and heat oven to 450 degrees. Toss cauliflower with 1 tablespoon oil, cumin, paprika, salt, and pepper. Spread cauliflower evenly over aluminum foil–lined rimmed baking sheet and roast until well browned and tender, 20 to 25 minutes. Let cool slightly, then transfer to large bowl.
Line clean rimmed baking sheet with parchment paper. Using potato masher, mash cauliflower until broken down into rough ½-inch pieces. Stir in panko, carrot, raisins, and egg until well combined. Divide cauliflower mixture into 4 equal portions. Using lightly moistened hands, tightly pack each portion into ¾-inch-thick patty and place on prepared sheet. Cover and refrigerate patties until chilled and firm, at least 30 minutes or up to 24 hours.
Heat remaining 2 tablespoons oil in 12-inch nonstick skillet over medium heat until shimmering. Using spatula, place patties in skillet and cook until deep golden brown and crisp on first side, 3 to 5 minutes. Using 2 spatulas, gently flip patties and cook until browned and crisp on second side, 3 to 5 minutes. Serve burgers on buns, topped with yogurt sauce, almonds, and arugula.
