Cheese and Herb-Stuffed Georgian Dumplings (Khinkali Qvelit)

Ingredients

• 4 cups (11/4 lb.) all-purpose flour, divided, plus more for dusting
• 1 1⁄4 tsp. kosher salt, plus more as needed
• 2 cups (1 lb.) ricotta, excess moisture strained and discarded
• 1⁄2 cup (4 oz.) sour cream
• 1⁄4 cup finely chopped cilantro
• 1⁄4 cup finely chopped fresh mint
• 3 large eggs, beaten
• Freshly ground black pepper