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Step 1
Drain the potatoes and add to a pot of water (potatoes should be covered by at least 1 inch). Cover and bring to a boil on high heat, then remove cover and continue boiling over medium-high heat until potato cubes are easily pierced with a paring knife (see Recipe Note #3).
Step 2
Drain the potatoes well in a colander and transfer to a mixing bowl. Add the butter and sour cream: mix with a spoon to allow the butter to melt before you start mixing. Add salt and pepper.
Step 3
Set an electric beater on low and mix the potatoes until all large chunks are broken up, about 35 seconds. Add milk and continue mixing until incorporated, about another 30 seconds. Taste to check the texture and seasoning, adjusting as needed. Do not overmix.
Step 4
Add in the horseradish (again, see Recipe Note #2); stir well with a spoon to incorporate.
Step 5
Serve, sprinkling each serving with chives (if you like).