Rinse the rice first, then boil it in 1 1/2 cups water for about 10 minutes. Add the milk and cook slowly over low heat for about 30 minutes, stirring often, until very thick and creamy. Stir in the salt at the end and set aside to cool.

Stir salt into the all-purpose flour, then add the water. Mix in the rye flour a little at a time until a dough forms. Knead briefly, then shape into a log about 2 inches across. Wrap well, cover with a damp towel, and let it rest for 2 hours.

Boil the eggs for 5 minutes, then cool them in cold water. Peel and chop them, mash with the softened butter and chives, and season with salt and pepper.

Preheat the oven to its highest setting (up to 536°F or 280°C) and line a baking tray with parchment paper. Cut 18 pieces from half of the dough log. Roll each piece into a very thin oval on a well-floured board, using extra rye flour as needed. Spoon cooled rice porridge into the center, fold ends, and pinch long sides to form a boat shape.

Bake the pies in batches for 12 to 15 minutes until the crust is crisp and brown flecks appear. Meanwhile, bring the water and butter for the glaze to a simmer, and dip or brush the hot pies with the butter water.

Serve warm with a generous spoonful of egg butter on top. Refrigerate leftovers for up to 3 days or freeze for up to 2 months.