1) To make the dough: Combine all the ingredients and mix and knead — by hand, mixer, or bread machine set to the dough cycle — until the dough is smooth and satiny.
2) Put the dough into a well-greased bowl and drizzle a little olive oil on it, to prevent the formation of a skin while it's rising. Cover with plastic wrap and let rise until doubled in volume, 1 to 2 hours.
3) To fill the braid: Combine the garlic and oil. Turn the dough out onto a lightly floured surface and knead to expel any air bubbles.
4) Roll the dough into an 18" x 12" rectangle. Brush an even coating of the garlic olive oil over the surface. Layer the Provolone, salami, and red peppers down the center 4" of dough.
5) To form the braid: Starting at the edge of the filling, make parallel horizontal cuts in the dough at 1" intervals down both sides, leaving a 1" border at the top and bottom. Fold the top and bottom edges over the filling.
6) Starting with the top right-hand strip of dough, fold it over the filling. Cross the top left-hand strip over the filling. Continue alternating strips to create a braided effect. Brush with the remaining garlic and olive oil mixture.
7) Gently pick the braid up and transfer it to a greased or parchment-lined baking sheet.
8) Cover the braid, and let rise until puffy, 30 to 60 minutes. Towards the end of the rising time, preheat the oven to 350°F.
9) Brush the risen braid with the glaze, then bake for 30 to 35 minutes, or until golden brown. Remove from oven and cool slightly before serving.
Yield: one 18" braided loaf, about 10 servings.