Heat the oil in large pot over medium heat. Add the shallots and cook briefly to soften, 3 to 4 minutes. Stir in the broccoli, and season with salt and pepper, to taste Add the chicken broth and bring to a boil. Reduce the heat to maintain a simmer, then cover the pan and cook until the vegetables are fork tender, 10 to 15 minutes. Cool for about 5 minutes. Carefully add the soup to a blender, in small batches, and blend until smooth. Pour the puree into a clean large saucepan over low heat. Add hot water to thin, if necessary. Whisk in all but 1/2 cup of the mascarpone. Taste and adjust the seasoning, as necessary.
To serve, ladle the soup into bowls and garnish each bowl with a small dollop of mascarpone.