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Blending the onion for 1 minute should be enough to puree the onion, but every blender works a little differently. If you still have notable pieces of onion in your blender, stop the blender, open the lid, and push the pieces down toward the blades using a rubber spatula. Replace the lid and continue blending at 30 second intervals at high speed until completely blended. The strainer should be small enough to fit inside the bowl, but if possible, large enough to rest on the lip of the bowl. Otherwise, hold the strainer over the mouth of the bowl with one hand.
Repeat blending as necessary. Position a strainer over the mouth of a bowl.