Make the custards:
Heat the oven to 350°F. Cut about 1/4 inch from the top of the garlic head to expose the cloves. Wrap the head in foil and bake until the garlic is very soft, about 45 minutes. When cool enough to handle, separate the cloves and squeeze the garlic from the skins into a blender or food processor.
Add the eggs, 1 tsp. salt, and 1/2 tsp. pepper to the roasted garlic and pulse until completely smooth. Pulse in the cream and broth.
Generously butter or oil six 4-oz. ovenproof ramekins and put them in a deep roasting pan. Divide the custard mixture among the ramekins and fill the roasting pan with enough boiling water to come three-quarters of the way up the sides of the ramekins.
Bake the custards until the centers are just set and the tops are very lightly browned, 35 to 40 minutes. Remove the ramekins from the water bath and cool on a rack to room temperature before unmolding.
Make the soup:
In a 4-quart saucepan, melt the butter over medium heat. Add the shallots or onions, fennel seed, red pepper flakes, and a big pinch of salt. Cook, stirring occasionally, until the shallots are tender but not brown, about 2 minutes.
Add the chopped asparagus spears and potatoes; cook for 1 minute. Stir in the broth and bring to a boil. Reduce the heat to medium low and simmer until the vegetables are tender, about 10 minutes.
Meanwhile, have ready a bowl of ice water. Bring a small pot of well-salted water to a boil over high heat. Add the asparagus tips and cook until tender but still bright green, about 2 minutes. Drain and then transfer the tips to the ice water to cool. Drain again and set aside.
Remove the soup from the heat, add the spinach, and stir until wilted. Working in batches, purée the soup in a blender. Return the soup to the stove. Stir in the crème fraîche and heat through. Season to taste with salt.
Run a knife around the edge of each custard, tap the sides of the ramekins with your hand to loosen the custards, and invert them onto a cutting board. Set out six wide-rimmed shallow soup bowls and carefully place one custard top side up in the center of each. Ladle the soup around the custards, garnish with the asparagus tips, and serve.
The custards can be made up to 1 day ahead; cover and refrigerate. Return to room temperature before serving.