In a large saucepan, place spinach in a steamer basket over 1 in. of boiling water. Cover and steam for 2-3 minutes or just until wilted. When cool enough to handle, squeeze spinach dry and finely chop.
In a nonstick skillet, saute the mushrooms, onion and garlic in oil until tender. Add spinach; cook and stir for 2 minutes. Transfer to a large bowl. Stir in the egg, cheese, bread crumbs, 1/4 teaspoon rosemary and salt until well blended.
Flatten chicken to 1/4-in. thickness. Combine the basil, thyme, pepper and remaining rosemary; rub over one side of chicken. Spread spinach mixture over plain side; roll up. Secure with toothpicks.
In a large saucepan, place roll-ups in a steamer basket over 1 in. of boiling water. Cover and steam for 12-15 minutes or until chicken is no longer pink.