Place the eggs in a saucepan and cover them with water. Bring to a boil over medium-high heat. Once boiling, cover the pan, remove it from heat, and let it sit for 12 minutes.
After 12 minutes, transfer the eggs to an ice bath to cool for about 5 minutes. Once cooled, peel the eggs and chop them into small pieces.
In a mixing bowl, combine the chopped eggs, feta cheese, mayonnaise, Greek yogurt, lemon juice, Dijon mustard, garlic powder, salt, and pepper. Mix until well combined.
Toast the slices of whole grain bread until golden brown.
Spread a generous amount of the egg salad mixture on each slice of toast.
Top with fresh arugula or spinach and garnish with sliced radishes if desired. Serve immediately.