Bring broth to a simmer in a medium saucepan (do not boil). Keep warm over low heat.
Cook peas in boiling water for 3 minutes or until crisp-tender. Drain and rinse with cold water; drain.
Heat oil in a large nonstick skillet over medium-high heat. Add leek and carrot; sauté 5 minutes or until tender, stirring frequently. Add rice; cook 3 minutes, stirring constantly. Stir in 1 cup broth; cook 5 minutes or until the liquid is nearly absorbed, stirring frequently. Stir in 1/2 cup broth, vermouth, salt, and oregano. Add remaining broth, 1/2 cup at a time, stirring frequently until each portion of broth is absorbed before adding the next (about 25 minutes). Add peas; cook 4 minutes. Stir in cheese and remaining ingredients.
Wine note: Why not mirror all the wonderful greeness of the sugar snap peas and leeks with a wine that's got its own green drama going on? A great bet, and a steal: Brancott Vineyards Sauvignon Blanc from Marlborough, New Zealand(about $10).