Sprinkle the yeast and sugar over the water in a large bowl. Let stand until the mixture looks foamy, about 10 minutes. Stir to dissolve the yeast. Stir in the melted butter and the salt. Gradually stir in enough of the flour to make a stiff dough. Turn out onto a lightly floured work surface. Knead, adding more flour as required, until the dough is smooth and elastic, about 10 minutes.
Gather the dough into a ball. Lightly oil a large bowl. Place the dough in the bowl and turn to coat with oil. Cover the bowl with a damp kitchen towel. Let stand in a warm placed until the dough has doubled in volume, about 1 hour.
Lightly oil two half cylinder shaped French bread pans or a large baking sheet. Punch down the dough. Turn out onto a lightly floured work surface and knead briefly. Divide the dough in half. Working with one portion of dough at a time, roll out into a rectangle 12 inches long and 8 inches wide. Spread with ½ cup of the pesto, leaving a ½ inch wide border on all sides. Starting at the long end, roll up into a tight cylinder and pinch the seams closed, tucking the ends under the loaf. Place on the baking sheet. Cover with a damp kitchen towel. Let stand in warm place until doubled in volume, about 45 minutes.
Meanwhile, position a rack to the center of the oven, preheat to 400 *F. Beat the egg with the ½ teaspoon of salt to make a glaze. Uncover the loaves and brush lightly with the egg glaze. Bake until the loaves sound hollow when tapped on the bottom, about 35 minutes. Transfer to a wire rack and cool.
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