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1. Make your starter. Dissolve 1/2 teaspoon yeast in 1 cup water. Once the yeast is dissolved, mix with rye flour and 1.5 cups all purpose flour until goopy. Cover and let sit at room temperature for at least 3 hours until starter has grown and is bubbly.
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2. In the bowl of a mixer (this is not a good dough to mix by hand), place all of the starter. Dissolve the second 1/2 teaspoon of yeast in 1/2 cup warm water and add it to the starter mixture. Beat on low for 30 seconds.
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3. In a bowl, mix 2 1/2 cups flour and salt. Using the paddle attachment, slowly add this to the starter until blended, about 3 minutes.
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4. Switch to dough hook if you have one, and knead on medium for four minutes until dough starts to gain some body. Add in your asiago cheese during this process. The dough will be soft and slightly sticky, but will mostly clean the sides when it's ready. When you pour it out of your bowl, it will kind of act like a big blob, but stick together.
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5. Generously spray or oil a rectangular or square container. The shape of your container is important - it makes a world of difference when shaping, allowing you to minimally touch the dough. Place the dough into your container, cover with floured cloth or oiled plastic wrap, and leave it until it doubles in size, approximately 1 to 2 hours. I let mine rise in the sun outside.
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6. Generously flour a surface. I emphasize generously.
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7. Your dough will have risen in a rectangular shape. Trying to preserve that shape as much as possible. Remove dough from container onto floured surface. It should be a lot easier to handle compared to before.
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8. Gently stretch your dough into a 12 by 8 rectangle, taking care not to deflate it much. You'll notice how much the square proofing container helps when doing this.
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9. Line two baking sheets with parchment paper, regardless of whether you are using a baking stone.
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10. Using a sharp knife or a dough scraper, cut your dough rectangle into 8 rectangular pieces. Don't drag your knife or scraper-just push down and cut. We're trying not to flatten the dough here.
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11. Piece by piece, gently place floured-side up roll onto baking sheets. Cover and let rise in warm room until puffy, about 45 minutes.
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12. In the meantime, preheat your oven to 450F, preheating your baking stones if desired.
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13. When ready to bake, sprinkle asiago cheese on top of each roll. Move your rolls to your baking stone on the parchment (the parchment makes it easy to slide on) or leave on baking sheets. Bake for 20-24 minutes, until golden brown. Let cool on rack.
