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Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess.
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In a large mixing bowl, or in the bowl of an electric mixer, combine all of the ingredients, mixing to form a shaggy dough. Knead the dough by hand (10 minutes) or by mixer (5 minutes) until it's smooth.
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Place the dough in a lightly greased bowl and allow it to rest for 1 hour; it'll become quite puffy, though it may not double in bulk.
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Gently deflate the dough and transfer it to a lightly oiled work surface. Divide the dough into 16 pieces (about 56g each) for dinner rolls, or nine pieces (about 100g each) for larger sandwich rolls. Roll each piece into a smooth ball.
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Arrange the dinner rolls evenly on a parchment-lined baking sheet, or place the sandwich rolls in a 9" square pan. (The sandwich rolls will touch one another once they've risen, creating soft-sided rolls.)
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Cover and let rise for 35 to 40 minutes, until noticeably puffy. While the rolls are rising, preheat the oven to 350°F.
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Brush the risen rolls with egg wash (the egg and water mixture) and sprinkle with oats.
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For smaller rolls on a baking sheet, bake for 21 to 24 minutes; for larger rolls in a square pan, bake for 30 to 32 minutes, until golden brown. Remove the rolls from the oven, and cool on a rack.
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Once they're completely cooled, wrap the rolls airtight and store at room temperature for several days; freeze for longer storage.
