In a small heavy saucepan cook leek with salt and pepper to taste in 1 tablespoon oil, stirring, until softened.
Add garlic, potato, and broth.
Simmer mixture, covered, for 8 to 10 minutes, or until potato is very soft.
Stir in fresh herbs and arugula, and allow the mixture to simmer covered, for 1 minute
In a blender, purée mixture in batches for 2 minutes or until completely smooth.
Transfer purée to a metal bowl set in a larger bowl of ice and cold water.
Stir in the half-and-half, salt, and pepper to taste
Then chill the soup, stirring occasionally, for 10 minutes or until cold.
While the soup is chilling, in a heavy small skillet cook bread cubes in the remaining 1 tablespoon oil until browned.
Transfer croutons to paper towels to drain and season with salt.
Divide soup between 2 bowls.
Top it with croutons and tomato.