Whisk the mayonnaise, ketchup and relish in a small bowl. Lay out 24 slices of bread and lightly spread one side of each with the mayonnaise mixture. Top 4 slices with lettuce and grilled mushrooms. Top with another slice of bread, mayonnaise-side up, followed by cheese, grilled eggplant and a third slice of bread, mayonnaise-side down. Set aside.
Top 4 more slices of bread with lettuce, cheese and marinated tomato. Top with another slice of bread, mayonnaise-side up, followed by marinated zucchini and radishes, and pickled onions. Top with the remaining 4 slices of bread, mayonnaise-side down.
Stack the eggplant clubs on top of the zucchini clubs to make a Dagwood, secure with a long skewer and top with an olive. Arrange the Dagwoods on a platter; dismantle into club sandwiches to serve.
Thinly slice 1 bunch radishes. Toss with the juice of 1 lemon and season with salt and pepper. Let marinate about 20 minutes.
Mix 1/2 cup olive oil, 3 minced garlic cloves and 1 teaspoon minced thyme. Thinly slice 1 eggplant. Brush with the garlic oil, season with salt and pepper and grill until charred, about 3 minutes per side.
Bring 1 1/4 cups red wine vinegar, 6 tablespoons sugar, 1/2 teaspoon fennel seeds, 1 bay leaf, a pinch of red pepper flakes and 1/2 teaspoon salt to a boil. Add 2 sliced red onions and simmer 1 minute; let cool.
Mix 1/2 cup olive oil and 3 minced garlic cloves. Scrape out the gills from 8 portobello mushroom caps, brush with the garlic oil and season with salt and pepper. Grill about 4 minutes per side.
Thinly slice 2 zucchini lengthwise. Lay on a platter, sprinkle with the zest and juice of 1 lemon and season with salt and pepper. Let marinate about 20 minutes.
Thinly slice 2 beefsteak tomatoes and sprinkle with 1 teaspoon salt and pepper to taste. Let marinate about 20 minutes.