I have an aeonium that I bought there a couple years ago. In
the last week the center of the main flower has protruded out like a
nose. Prior to this the leaves laid flat.

Is this normal/healthy? Is this a growth spurt?

Thanks for your help, Michael

Michael,
Your Aeonium is about to bloom. Congratulations! Anyway, the rosette will extend and turn into a large pyramidal shape covered with little yellow flowers. This can be very pretty, but it also takes so much energy from the plant it can kill the whole plant.

You can enjoy the giant pyramid bloom stock, and hope the rest of the plant survives, or you can go ahead and cut off the blooming rosette right now, which will save the plant, and leave you with a low shrubby plant for now.

Cut the stem for that one rosette off down low, and you can place the large cutting in a vase and enjoy the blooms that way. Spray the cut end on the plant with household hydrogen peroxide to help it heal, and it should branch from that point later in the winter.
Peter