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1
To make the dough, put 2 1/2 cups of the flour, salt, and all but 1 tablespoon of the sugar in the bowl of an electric mixer fitted with the dough-hook attachment.
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2
Put the yeast and 1 tablespoon warm water and the reserved tablespoon of sugar in a small bowl, and stir just until the sugar and yeast have dissolved.
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3
With the mixer, using the dough hook on low speed, pour into the bowl the yeast mixture, the milk, and the egg and egg yolks.
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4
Knead the dough until it is smooth, shiny, and elastic, about 10 minutes, adding more flour as needed.
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5
Add the pieces of butter a little at a time, until it is incorporated, then knead the dough on low speed for about 5 minutes, until it is silken and rich.
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6
Transfer it to a large, greased bowl, cover with plastic wrap, and allow it to rise for 2 hours.
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7
When the dough has risen, press it down, and put it in a plastic bag or wrap it in plastic wrap.
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8
Refrigerate for 1 to 2 hours or overnight.
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9
To make the tapenade filling, put the olives, half the anchovies, the fennel seeds, and 1 tablespoon of the olive oil in the bowl of a food processor fitted with a steel blade.
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10
Puree the mixture until it is smooth.
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11
Taste, and if you want, add more anchovies or salt, and another tablespoon of olive oil if the filling is not smooth enough.
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12
When ready to assemble the babkas, grease two 9-inch round pans.
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13
Take the dough from the refrigerator and divide it in half.
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14
On a lightly floured surface, roll out one piece into a 16-by-12-inch rectangle.
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15
Using a knife or an offset spatula, spread half of the olive-anchovy filling very thinly over the dough, leaving a 1/2-inch border all around.
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16
Beginning with the long side, tuck in the ends and roll the dough up tightly.
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17
Cut the rolled-up dough into twelve equal pieces, and place them, with one of the cut sides of each facing up, in one of the pans in one layer.
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18
Repeat with the remaining dough and filling in the other pan.
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19
Allow the babkas to rise, covered with a towel, for 2 hours before brushing with the reserved 2 tablespoons melted butter.
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20
Preheat the oven to 350 degrees, and bake for 25 to 30 minutes, or until golden.
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21
Once the rolls are cool enough to handle, pull them apart gently into individual babkas.
