In a large colander over a bowl or the sink, drizzle 1/2 cup water over the toasted bread to saturate. Squeeze the bread with your hands to remove any excess liquid, then crumble into bite-size pieces. Transfer to a large serving bowl and drizzle with 1/2 cup olive oil; season to taste with salt and pepper.
Add the tomatoes, cucumber and salami to the bread and toss to combine. Add the basil and drizzle the red wine vinegar and remaining 1/2 cup olive oil on top. Toss and season to taste with salt, pepper and more olive oil.