TO MAKE THE PASTE: Combine the water and tomatoes in a small saucepan over medium-high heat. Bring to a boil and cook until softened, about 5 minutes. Drain well. Transfer to a food processor or blender, add the olive oil, garlic, salt and pepper, and process. Puree until the mixture is smooth, about 15 seconds. Set aside.
TO MAKE THE PESTO: Combine all the ingredients in a food processor or blender and process until the mixture is smooth, about 15 seconds. Set aside.
TO MAKE THE TAPENADE: Combine all its ingredients in a food processor or blender and process until the mixture is smooth, about 15 seconds. Set aside.
TO MAKE THE DOUGH: Combine the yeast, sugar, and water in the bowl of an electric mixer fitted with a dough hook. Beat on low speed for 1 minute. Add the sun-dried tomato paste (or pesto or tapenade), salt, and flour. Beat at low speed until all of the flour is incorporated, about 1 minute. Then beat at medium speed until the mixture forms a ball, leaves the sides of the bowl, and climbs up the dough hook. Remove the dough from the bowl. Using your hands, form the dough into a smooth ball. Lightly oil a bowl. Place the dough in the bowl and turn it to oil all sides. Cover with plastic wrap and set aside in a warm, draft-free place until it doubles in size, about 1 hour. Preheat the oven to 350 degrees F.
TO ASSEMBLE: Remove the dough from the bowl and invert it onto a lightly floured surface. Pat the dough into a rectangle about 3/4-inch thick. Roll up the dough, beginning with the short side and stopping after each full turn to press the edge of the roll firmly into the flat sheet of dough to seal. Press with your fingertips. Tuck and roll so that any seams disappear into the dough. Join the ends of each bread loaf and pinch all three together. Begin braiding, lapping each loaf one at a time over the other, then pinch the remaining ends together. Tuck the pinched ends underneath the braided bread. Line a baking sheet with parchment or waxed paper. Place the bread on the baking sheet. Cover with plastic wrap and set aside in a warm, draft-free place until it doubles in size, about 1 hour. With a pastry brush, brush the beaten egg evenly over the bread. Combine the kosher salt and pepper and sprinkle over the top of the bread. Bake until lightly brown, 45 to 50 minutes. Remove from the oven and cool on a rack.