Sauté ham and shallots in oil in a large pot over medium-high heat, stirring often, until shallots are golden, 4 to 6 minutes. Stir in broth and zest. Cover and bring to a boil; then reduce heat and simmer, covered, 15 minutes to blend flavors.
Stir in greens and return to simmering; then cook, covered, until tender, 10 to 15 minutes. Stir in mushrooms and cook just until wilted, 1 to 2 minutes. Season to taste with salt and pepper.
Ladle soup into bowls, discarding lemon zest if you like.
*For easiest prep, slide fingers down stems to remove ribs, chop and measure leaves, then rinse.