Activate the Yeast: Sprinkle the active dry yeast over 1 cup (237 milliliters) of the lukewarm water in a small bowl, stir to combine, and let it stand for about 10 minutes, until frothy.
Mix the Dough: Combine the flour, sugar, and fine salt in the bowl of a stand mixer fitted with a dough hook or in a large bowl. Slowly incorporate the yeast mixture and melted, slightly cooled butter. Adjust the Dough: Gradually add the remaining 1/4 cup (60 milliliters) lukewarm water as needed to form a soft dough.
Knead Until Smooth: Transfer the dough to a lightly floured surface and knead until it becomes smooth and elastic.
First Rise: Place the kneaded dough in a large bowl, cover it with plastic wrap or a towel, and let it rise for 1–2 hours, or until it has doubled in size.
Prepare the Baking Sheets: Line two baking sheets with parchment paper or lightly grease them.
Divide the Dough: Once the dough has doubled, transfer it to a lightly floured surface and divide it into 10 equal portions.
Shape the Rolls: Shape each portion into a smooth oval, tucking the seams underneath, then arrange the shaped rolls on the prepared baking sheets.
Rest the Rolls: Cover the shaped dough and let it rest at room temperature for 30 minutes.
Preheat the Oven: Preheat the oven to 425°F (220°C).
Prepare the Baking Soda Bath: Place 8 cups (2 liters) of water and the baking soda in a pot and bring the mixture to a boil.
Boil the Rolls: Reduce the water to a low boil and gently place the dough pieces into the baking soda solution, working in batches if needed so they are not overcrowded. Turn each piece to coat all sides, boil for 30 seconds, then lift it out with a slotted spatula and return it to the prepared baking sheet. Make the Egg Wash: Beat the large egg together with 1 tablespoon (15 milliliters) of water in a small bowl.
Brush the Rolls: Brush the tops and sides of each boiled roll thoroughly with the egg wash.
Add the Salt: Sprinkle coarse sea salt over the egg-washed rolls.
Score the Tops: Using a sharp knife, lightly make two slits across the top of each roll, running from the long side to the long side.
Bake Until Golden: Place the rolls in the preheated oven and bake for 15–18 minutes, until the surfaces are golden brown.
Cool the Rolls: Transfer the baked rolls to a wire rack and allow them to cool to room temperature.
Serve Fresh: Enjoy the Silserli on the day they are baked, when they are at their best.