Preheat the oven to 450 degrees F. Lightly grease a large baking sheet and set aside.
Remove the dough from the bowl. On a lightly floured surface, knead briefly. Let rest for 10 minutes. Roll out into a rectangle, about 16 by 10 inches, and cut into six squares, about 5 inches each. Lightly brush each square with olive oil, leaving a 1/4-inch border. Bake until starting to turn light golden brown, about 6 minutes. Evenly cover each square with goat cheese and return to the oven until the crust is golden brown and slightly crisp and the cheese is melted, 2 to 4 minutes.
Remove from the oven and let cool slightly. Cut each square in half diagonally. Arrange smoked salmon on each pieces and top with a dollop of salmon roe. Sprinkle with shallots, garnish with a small sprig of dill, and serve immediately.
1 cup warm (110 degrees F) water
1 (1/4-ounce) envelope active dry yeast
1 teaspoon sugar
1 tablespoon plus 1 1/2 teaspoons extra-virgin olive oil
3 cups bleached all-purpose flour
1 teaspoon salt
In a large bowl, combine the water, yeast, sugar, and 1 tablespoon oil and stir to combine. Let sit until the mixture is foamy, about 5 minutes.
Add 1 1/2 cups of the flour and the salt, mixing by hand until it is all incorporated and the mixture is smooth. Continue adding the flour, 1/4 cup at a time, working the dough after each addition, until all the flour is incorporated but the dough is still slightly sticky. Turn the dough out onto a lightly floured surface and knead until smooth but still slightly tacky, 3 to 5 minutes.
Oil a large mixing bowl with the remaining 1 1/2 teaspoons olive oil. Place the dough in the bowl and turn to oil all sides. Cover the bowl with plastic wrap and set in a warm, draft-free place until nearly doubled in size, 1 to 1 1/2 hours.
Use as directed.
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