Put the 1/4 cup olive oil and the garlic slices in a large skillet and place over medium heat. When the garlic starts to turn a light golden brown, add the broccoli rabe, 3/4 teaspoon salt and a few grinds of pepper. Stir to coat evenly in the oil. Cover the skillet with a lid and turn the heat down to low. Cook until the broccoli rabe stems are just tender, 6 to 8 minutes. Uncover and turn the heat up to medium-high. Stir in the cherry pepper pickling liquid and cook until the pan is dry, an additional 3 to 4 minutes. Transfer to a bowl and let cool completely.
Slice the semolina loaf horizontally and lay the two halves cut-side up. Pull out some of the bread from both halves (reserve for another use), leaving a 1/2--inch border. Drizzle both halves with some olive oil. Spread half of the broccoli rabe on the bottom half. Layer on the cherry peppers, provolone, prosciutto, salami, mortadella, the remaining broccoli rabe and the top half of bread. Wrap tightly in parchment, wax paper or plastic wrap and tie with twine if necessary. Place a brick (see Cook's Note) or cast-iron skillet on top for at least 3 hours to flatten, refrigerated. About 45 minutes before serving, bring the sandwich to room temperature.
A brick that weighs about 4 pounds works best. Wrap it in foil to protect kitchen surfaces, if desired.
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