Whisk the all-purpose flour, rye flour, and salt together in a mixing bowl. Add the warm water and 1 tbsp olive oil, and mix with a wooden spoon until a rough dough forms.

Turn the dough onto a floured surface and knead for 8 to 10 minutes until smooth and elastic. Shape into a ball, cover with a damp towel, and rest at room temperature for 30 minutes.

Heat 1 tbsp olive oil in a 26 cm / 10-inch skillet over medium heat. Add the speck and onion, and cook for 4 to 5 minutes until the onion softens and the speck starts to crisp.

Stir in the garlic and caraway seeds and cook for 1 minute until fragrant.

Add the sauerkraut and cook for 5 minutes, stirring often, until most of the liquid has evaporated.

Add the spinach and cook for 3 to 4 minutes until wilted and any extra liquid has cooked off. Season with black pepper and set aside to cool to room temperature, about 15 minutes. Hot filling will tear the dough.

Divide the rested dough into 10 to 12 pieces, about 50 g each. On a lightly floured surface, roll each piece into a thin round, roughly 12 cm / 5 inches across and 2 mm thick.

Spoon about 1.5 tbsp of the cooled filling onto one half of each round. Fold the dough over into a half-moon shape and press the edges firmly with your fingers or a fork to seal.

Pour the sunflower oil into a 2.8 L / 3-quart pot or dutch oven, about 5 cm / 2 inches deep. Heat to 175 C / 350 F on a candy or instant-read thermometer.

Fry the tirtlen in batches of 2 to 3 so the oil temperature doesn't drop. Cook for 2 to 3 minutes per side, turning once, until deep golden brown and puffed.

Lift out with a slotted spoon and drain on a wire rack lined with paper towels. Let the oil return to 175 C / 350 F between batches.

Serve warm, on their own or with a small bowl of sour cream for dipping.