Combine the flour, yeast, rosemary, sugar, and salt. Add the water and olive oil. Using an electric mixer on medium speed, beat for 1 minute. (Dough will be sticky.)
Divide the dough among the prepared muffin cups, using about 2 teaspoons per cup. Let rise in a warm, dry place until doubled (about 30 minutes).
To make the topping and bake the rolls:
Preheat oven to 375°F (190°C).
Stir together the olive oil, rosemary, and salt in a small saucepan. Cook over medium-low heat until the oil is hot and the rosemary is fragrant (about 90 seconds). Set aside to cool.
Brush or spoon the cooled olive oil mixture over each roll in the muffin pans.
Bake 20 to 25 minutes, or until the rolls are golden brown.