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1
Make dressing: in a bowl, whisk together vinegar, garlic, dill, mustard, and salt and pepper until well combined.
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2
Whisking constantly, add 1/4 cup oil in a thin, slow stream.
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3
If the dressing still looks separated after all the oil has been added, a little more mustard whisked in should do the trick.
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4
Set dressing aside.
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5
Make cakes: in a bowl stir together potato, beet, carrot, and onion.
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6
Add flour and egg and mix well.
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7
Heat 2 tablespoons oil in a skillet over medium-high heat.
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8
When a drop of water sizzles in the oil, you're ready: take about 1/4 cup of the beet mixture and flatten it out in the oil.
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9
Put as many cakes in as you can without crowding the pan.
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10
Once you've got them all in, cover and let cook 3-4 minutes.
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11
Uncover, flip, re-cover, and cook the other sides 2-3 minutes.
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12
Fry remaining mixture in batches.
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13
Serve with a liberal amount of vinaigrette and a dollop of sour cream, if desired.