I have had a couple of Persistent Penelopes in my time. The thing about these students that is so frustrating is that they fool you. You start out thinking you have a great student who is excited and interested in your class. Then you find out that what they really want is hand-holding. They want you to walk them through as much of the material as possible.
My solution to this type of student has generally been to tell them that I want to see their ideas. I know my own ideas, and I know that I know the material. I want to see them apply it, not just mimic what they think I want to hear.
The Penelopes of the world have the potential to be great students. I think that sometimes they just lack confidence. They are afraid that their own ideas and insights are not "correct" so they try to get us to tell them exactly what to do. Penelope needs to learn that her ideas have merit in and of themselves. Baby birds sometimes need to be dropped out of the nest so they can learn to fly on their own.
Cut Penelope off. Tell her you will not walk through every detail of the assignments with her. Give her guidance, but let her do the work. Drop her out of the nest and tell her you want to see what she comes up with on her own.