Make the flan: Preheat oven to 325 degrees. Generously butter six 6-ounce ramekins, and place in a roasting pan. Combine cream and milk in a bowl.
Bring a medium pot of water to a boil. Add 1 tablespoon salt and the peas. Reduce heat, and vigorously simmer until peas are very tender, about 5 minutes. Drain, and immediately transfer to a food processor. Add butter, 1 tablespoon cream mixture, and 3/4 teaspoon salt. Puree until very smooth, 2 to 3 minutes.
Pour puree through a coarse sieve. Measure out 1/2 cup strained puree into a bowl, and whisk in eggs, then remaining cream mixture. Strain through a fine sieve (this will result in the finest-textured flan). Divide among ramekins.
Bring a kettle of water to a boil. Place pan in oven, and add enough boiling water to pan to reach halfway up sides of ramekins. Bake until custards are almost completely set (the centers should still wobble, but not be liquid), 25 to 30 minutes.
Using tongs, transfer ramekins to a wire rack and let cool 30 minutes. Serve warm, at room temperature, or cool (flans can be refrigerated in ramekins up to 1 hour); dip bottoms in hot water to loosen before unmolding.
Make the mushrooms: When ready to serve flans, melt butter in a large skillet over high heat until foamy. Add mushrooms and lemon zest; season with salt and pepper. Saute until mushrooms are golden brown and tender, stirring once or twice, 3 to 4 minutes. Stir in scallions, and saute 1 minute more. Add cream, and cook 1 minute. Stir in parsley and lemon juice. Season with salt and pepper.
Serve flans with sauteed mushrooms and lemon wedges. Garnish with lemon-zest strips.