In a medium saucepan, heat milk and butter over medium-low heat until butter is melted and mixture registers 100°F/38°C to 105°F/41°C on an instant-read thermometer. Remove from heat; stir in syrup and yeast until dissolved.

In a large bowl, whisk together rye flour and salt; stir in yeast mixture until well combined. Add all-purpose flour, and stir until dough is firm and no dry bits remain. Knead dough until smooth and elastic, about 10 minutes; cover and let rise in a warm, draft-free place (75°F/24°C) until nearly doubled in size, about 1 hour.

Divide dough into 6 to 8 portions (about 70 grams each). On a lightly floured surface, roll each portion into a 7½-inch circle. Cover and let stand in a warm, draft-free place until relaxed and slightly puffed, about 30 minutes.

Heat a 10-inch cast-iron skillet over medium-high heat. Add 1 to 2 tablespoons (14 to 28 grams) oil; add dough round, one at a time. Cook until browned on both sides, about 1 minute per side. Repeat with all dough, adding oil as needed. Let dough cool on a wire rack.

In the bowl of a food processor, pulse almonds until coarsely ground. Add sugar, egg whites, and salt; process until mixture is well combined and forms a thick paste. Transfer to a medium bowl, and let stand at room temperature until mixture thickens but is still spreadable.