For the tomatoes: In a shallow bowl, mix the tomatoes, green onions, parsley, basil, garlic, olive oil and vinegar. Season with salt and pepper. Cover the bowl and let the tomatoes marinate at room temperature for at least 1 hour, but preferably 3 to 4 hours. Stir them occasionally so that all the tomatoes are marinated. If the tomatoes are very ripe and marinate long enough, they will crack and burst, allowing their juices to mix deliciously with the marinade.
For the garlic bread: Combine the olive oil and garlic and let the mixture stand for 10 minute so the flavors blend. Meanwhile, heat the broiler. Brush one side of each piece of bread with the garlic and olive oil and broil them, oiled side up, until lightly browned. Put a slice of provolone and a generous sprinkling of asaigo on the toasted side of each slice, saving a little Parmesan for garnish. Set the bread aside until you're ready to serve the tomatoes.
Just before serving, heat up the broiler again. Toast the bread under the broiler until the cheese is bubbly.
To serve, put a piece of the bread in a shallow soup bowl. Spoon about 3/4 cup of the tomatoes and marinade on or around the edges of the bread. Garnish with more asaigo.