In a large mearsuing cup, combine the yeast, sugar, and 1/2 cup of the water and stir to dissolve. Allow to stand for about 10 minutes, or until the yeast mixture forms a frothy head. (If no head forms, the yeast is bad. Discard the mixture and start again with fresh yeast.) Stir in the remaining 1/2 cup water and the olive oil.

In the bowl of a food processor fitted with the metal blade, combine the all-purpose flour, whole wheat flour, polenta, rosemary, orange zest, and salt and process in several short bursts to combine. With the motor running, add the yeast mixture through the feed tube in a steady stream, taking about 10 seconds to pour it in. Continue to process for 10 seconds more, by which time the dough should have formed a ball on the stem. If the dough is too wet and forms a ball right away, remove the cover and sprinkle 2 tablespoons of all-purpose flour over the dough. Or if it is too dry and has not formed a ball on the stem within 15 seconds, sprinkle over 1 to 2 tablespoons more water. Process in 5-second bursts 3 more times, then turn the dough out onto a lightly floured board and knead for 1 minute. The dough should be slightly soft but not sticky.

Begin stretching, pushing, and pulling the dough with your fingertips and the heel of your hand into an 8 x 12-inch rectangle. This will take a while as the dough will be very tight at first. Be patient: Within about 5 minutes it will soften up and acquiesce. Transfer the dough to a generously oiled baking sheet and brush the top of the dough with more oil. Cover with a tea towel and allow to rise in a warm, draft-free place for about 45 minutes, or until puffy.

Preheat oven to 400°F.

Transfer the dough to an unfloured cutting board and cut it crosswise into 4 equal sections. Cut them crosswise into 8 little strips and roll each one under the palms of your hands into a thin rope about 12 inches long. Transfer to oiled baking sheets. Do this in batches if necessary, keeping the unrolled strips covered with the towel and rolling them out just before baking. Brush with beaten egg and sprinkle with fennel seeds and coarse salt to taste.

Bake 15 minutes or until slightly golden. Serve warm with a little dish of your best extra virgin olive oil or cool on racks. (The breadsticks will keep in an airtight container for up to 2 weeks. To serve them after they have been stored for a few days, reheat on a dry baking sheet, uncovered, at 350°F for 20 minutes.)