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Use whatever strainer you have: Perhaps a fine-mesh, a collander set over another pot or — if you happen to inexplicably have access to a restaurant — a tamis or a chinois.

Peel the cooked potatoes with a paring knife and pass them through a tamis or a potato ricer into a bowl.

When blending, a high-speed Vitamix is an excellent option — a standard food processor may not break down the onion as well as possible, so straining through a tamis or fine-mesh strainer after blending is a necessary step in that case.

The tamis is a round, drum-shaped utensil with a flat mesh bottom.

Especially soft foods can be pressed through the fine holes of a tamis using a dough scraper.