Melt the butter in a medium saucepan over medium heat. Add the onion and 3/4 teaspoon salt and cook, stirring often, until tender, 6 to 8 minutes. Add the broth and bring to a boil.
Place the peas and mint in a blender and add the hot broth mixture. (Because hot liquids expand when blended, hold the lid firmly in place with a kitchen towel before blending.) Blend until smooth. Return to saucepan to heat through, if necessary.
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