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Melt the butter in a large Dutch oven over medium heat. Add the onion and 1/2 teaspoon salt and cook until the onion is softened, about 5 minutes, stirring occasionally.
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Add the flour and cook for 1 minute while stirring. Slowly add the broth, scraping up any browned bits. Bring to a simmer and cook for 5 minutes.
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Add the peas to the soup and simmer until tender, 5 to 7 minutes.
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Puree the soup in batches in a blender (or food processor) until smooth.
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Return the pureed soup to the pot and stir in the cream. Bring to a brief simmer, then remove from the heat. Season with salt and pepper to taste before serving.
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To Make Ahead.
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This soup can be prepared through step 2, cooled, covered, and refrigerated for up to 3 days. It cannot be frozen. Reheat over low heat and proceed with step 3.