Right: here is my definitive version. Sorry to bang on about it; but eggs Florentine is one of my favourite dishes. Previous posts are here and here; this one trumps them, because it ensures that each component is cooked for the right length of time and no longer.
Place gratin dish in warm oven. Heat saucepan or frying pan of water for the eggs. No salt or vinegar (see why in the comments section here). Crack eggs into cups. Wash spinach. Grate cheese.
Make bechamel (there's a recipe in the 11.6.07 entry). Season, and leave to simmer over a very low light above a heat disperser, stirring from time to time.
Transfer wet spinach to saucepan, clamp on lid, and place on high heat. Lower eggs into simmering water; turn down heat to lowest setting.
The spinach should have started to wilt. Take off the lid, and stir, until all the leaves are wilted and cooked. Transfer the spinach to a colander, and push it against the sides with a wooden spoon, to squeeze out the water. When you think you have done a decent job of that, take the gratin dish out of the oven, and lay the spinach in it. Grind over some salt and pepper.
The eggs should be poached by now. Lift them from the water with a slotted spoon, and lay them on the spinach. Stir the cheese into the bechamel; pour the sauce over the spinach and eggs. Put the dish under a hot grill for a minute or two, until the sauce bubbles and browns on top.