Preheat a grill to medium high. Toss the zucchini with a generous pinch of salt in a colander; set aside.
Brush the mushrooms, onion and bell pepper with 1 tablespoon olive oil; season with salt and pepper. Brush the bread slices with 1 tablespoon olive oil; season with salt and pepper.
Oil the grill grates. Grill the vegetables, turning, until tender, 6 to 10 minutes. Grill the sausages, turning, until marked and cooked through, 10 to 12 minutes. Toast the bread on the grill, 1 to 2 minutes. Chop the vegetables and sausages and transfer to a medium bowl. Add the cheese and 1/4 cup basil and toss; season with salt and pepper.
Squeeze the zucchini to remove any excess liquid; transfer to a bowl and toss with the artichoke hearts, remaining 1/2 cup basil and 1 tablespoon olive oil and the vinegar. Season with salt and pepper.
Cut the bread slices in half and top with the sausage mixture; drizzle with olive oil and top with basil. Serve with the zucchini salad.