Place onions in a 5- to 6-quart pan; cover with water. Bring to a rolling boil over high heat. Drain in a colander.
When onions are cool enough to handle, trim off ends. To remove peel, pinch each onion with your index finger and thumb (the onion should squirt from the outside layer).
In the same pan, combine shelled peas and 1 cup water. Cover and bring to boiling over high heat. Cook, covered, over medium heat for 2 minutes. Stir in sugar snap peas and Chinese pea pods. Cover and cook until peas turn bright green and are tender-crisp to bite, 2 to 4 minutes. Drain in a colander.
Quickly melt butter in the 5- to 6-quart pan over high heat. Stir in rosemary and onions. Turn heat to low, add pea mixture, and mix gently until warm, 2 to 3 minutes. Add salt and pepper to taste.