Put morels in a microwave-safe bowl; add broth and heat in a microwave oven on full power (100%) until steaming, 6 to 8 minutes. Let stand until morels are pliable, at least 10 minutes.
As morels soak, discard any dirt and debris from fresh mushrooms; trim and discard bruised spots and discolored stem ends (including stems from shiitakes). Quickly immerse mushrooms in water and swish to wash, then lift out and drain (avoid saturating them; they are like sponges). Cut mushrooms wider than 1 inch into 1/4-inch-thick lengthwise slices; leave smaller ones whole.
Melt butter in a 10- to 12-inch frying pan over high heat. Add fresh mushrooms, shallots, thyme, and sage; stir often until liquid is evaporated and mushrooms are browned, 8 to 10 minutes.
Meanwhile, with your hand, squeeze morels in broth to release grit. Lift out and squeeze dry. Carefully pour morel soaking broth into a glass measure without disturbing sediment; leave sediment behind and discard. Measure soaking liquid; if there's less than 1 3/4 cup, add enough water to make this amount. Pour into frying pan. Rinse bowl, return morels to it, cover generously with water, and squeeze morels in water to release any remaining grit. Lift out and squeeze dry; discard water. Add morels to frying pan and heat until simmering.
Rinse fennel; trim off and discard stalks (reserving feathery green leaves), stem end, and bruised spots. Thinly slice fennel head crosswise. Chop 1/4 cup feathery leaves and reserve a few sprigs (discard remainder); cover separately and chill.
In a 4 1/2-quart or larger electric slow-cooker, combine fennel, potatoes, and turnips. Pour hot mushroom mixture over vegetables; add wine. Cover and cook until vegetables are very tender when pierced, 5 to 5 1/2 hours on low, 4 to 4 1/2 hours on high.
In a small bowl, mix cornstarch and cream. Turn cooker to high. Add cornstarch mixture, reserved chopped fennel leaves, and spinach; stir occasionally until sauce is bubbling, 10 to 12 minutes. Season to taste with salt and pepper.
Spoon mushroom-vegetable stew into deep soup bowls (about 2-cup capacity). With a wide spatula, set a hot gruyère pastry on stew in each bowl. Garnish, if desired, with reserved sprigs of green fennel leaves.