Add eggs to a pot and cover with water. Bring to a boil, then steam for 13 minutes. Transfer immediately to an ice bath. Once cooled, peel the eggs.
Make the homemade mayo by adding the egg, lemon juice, and Dijon mustard to a jar plus a pinch of salt. Pour in the oil and use an immersion blender, starting at the bottom, until thick and creamy.
Slice eggs in half lengthwise and remove yolks. Add yolks to a food processor along with 2 tablespoons of homemade mayo, garlic powder, onion powder, smoked paprika, sweet relish, yellow mustard plus salt and pepper to taste. Blend until completely smooth.
(Optional) To dye the egg whites, boil chopped beets in water with vinegar for 10 minutes. Strain and cool the liquid. Add egg whites and soak for 5 minutes, then remove and pat dry.
Transfer filling to a piping bag with a tip and pipe evenly into egg whites. Garnish with fresh dill and edible flowers. Serve immediately or chill until ready.