Place the potatoes in a large pot and cover with water. Boil over high heat until fork tender, about 10 minutes. Drain under very cold water and let rest to dry.
As the potatoes are cooking, peel the eggs and separate the yolks from the whites. Chop the egg whites and set aside. Crush the yolks into a fine powder or use a wooden spoon to press them through a fine metal strainer into a large mixing bowl.
Add the mayonnaise, mustard, vinegar, garlic, salt, paprika, and pepper to the bowl with the egg yolks. Whisk to combine.
Add the cold potatoes to the dressing in the bowl and stir to coat the potatoes. Add the green onions, red onions, and chopped egg whites. Stir to combine.
Garnish with additional green onions and sprinkle lightly with paprika. Serve immediately or cover and refrigerate until ready to serve. Enjoy!
Notes
COOK'S NOTE: For perfectly smooth and creamy deviled eggs, place the yolks in a metal strainer. Use a wooden spoon to quickly press them through the strainer. They will be almost powdery. Scrape the strainer clean and stir in the fillings of your choice!