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1
Place ricotta in strainer set over medium bowl. Chill until ricotta has texture of wet clay, about 1 hour.
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2
Mix ricotta, 1/2 cup flour, egg, and next 5 ingredients in medium bowl, adding more flour by tablespoonfuls until dough is slightly sticky (do not add more than 4 tablespoonfuls). Cover and chill 30 minutes.
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3
Sprinkle rimmed baking sheet generously with flour. Transfer dough to lightly floured surface. Cut into 4 equal pieces. Using hands, roll 1 piece on floured surface into 3/4-inch-wide log. Cut log crosswise into 1-inch pieces. Place gnocchi on prepared baking sheet, spacing apart. Repeat with remaining dough. Cover gnocchi with plastic wrap and chill at least 1 hour and up to 1 day.
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4
Heat olive oil in large skillet over high heat. Add mushrooms; saute until beginning to brown, about 4 minutes. Add chopped white and pale green parts of green onions. Saute 1 minute. Add wine; stir until almost all liquid is absorbed, about 30 seconds. Add 1/2 cup chicken broth. Stir until sauce is slightly thickened, about 1 minute. DO AHEAD:
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5
Let stand at room temperature.
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6
Working in 2 batches, add gnocchi to large pot of boiling salted water, stirring to prevent sticking. Boil until gnocchi rise to surface of water, then continue boiling until cooked through, 1 1/2 to 2 minutes longer. Using slotted spoon, transfer gnocchi to skillet with mushrooms. Add sliced dark green parts of green onions.
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7
Rewarm mushrooms with gnocchi and green onions over medium heat, adding more broth by 1/4 cupfuls if dry. Remove from heat. Add 1/4 cup cheese, butter, and marjoram; stir until cheese and butter melt. Season with salt and pepper. Transfer to plates and sprinkle with additional cheese.
