Put the potatoes through a kitchen gadget

• Not quite mashed
• Chopped finely, as food
• Like not-quite-mashed potatoes
• Finely chopped, as potatoes
• Prepped for mashing, in a way
• Reduced to grains
• Finely chopped
• Put through a sieve

Wiktionary Word definitions in Wiktionary
vb. (en-past of: rice)