Preheat the oven to 450° F with two racks close to the center.
Slice the eggplants ¼-inch thick. Line a baking sheet with parchment and spray generously with cooking spray.
Arrange eggplant slices in a single layer. Spray tops of slices with cooking spray and sprinkle with ½ teaspoon of the salt.
Place in preheated oven. Bake for 30 minutes, flipping the slices at the halfway point.
While the eggplant begins to bake, prepare the portobellos. Remove stems and, using a small spoon, scrape the gills off the underside of the mushroom caps. Slice caps ¼-inch thick.
In a small bowl, whisk together olive oil, lemon juice, smoked paprika, and remaining ½ teaspoon salt.
On a second parchment-lined baking sheet, toss the portobello slices with the marinade. Arrange in a single layer and add to oven. Bake for 20 minutes.
Cut across the beltline of the boule. Use your hands to tear most of the soft insides out of both halves of the bread, leaving about ¼- to ½-inch barrier before the crust.
Spread the olive tapenade inside the bottom half of the bread and the pesto inside the top half.
Spread giardiniera in a thick layer on top of pesto.
Arrange the roasted portobello pieces in a compact layer on the bottom of the bread.
Layer on the eggplant, roasted peppers, and provolone.
Replace the top half of the bread and press down firmly a few times to make it nice and compact.
Let sit for at least an hour, or wrap and store for up to 12 hours if desired, then slice into wedges and serve.