Preheat the oven to 355°F (180°C), using a convection setting if available.
In the bowl of a stand mixer, combine the flour, yeast, oats, honey, eggs, and water. Attach the dough hook and mix on medium speed. Once the ingredients begin to come together, add the butter and salt. Continue kneading for about 15 minutes, until the dough is smooth and elastic.
Transfer the dough to a lightly greased bowl, cover, and let rise until doubled in size.
Once risen, turn the dough out onto a floured surface and divide it into 14 equal portions. Roll each portion into a rectangle, then tightly roll into a log shape to form long, slender rolls.
Arrange the rolls on a parchment-lined baking sheet, spacing them evenly. Let them rise at room temperature until doubled in size, about 30-50 minutes.
Brush the tops with the beaten egg and sprinkle with rolled oats. Bake for 15-20 minutes, or until golden brown.
Remove from the oven and let cool before serving. These rolls are perfect for sandwiches or simply enjoyed with butter.
Store in an airtight bag at room temperature for up to 5 days, or freeze for up to a month.