Place the eggs in a large pot and fill the pot with enough water to cover the eggs by one to two inches. Bring to a simmer, but not a full boil in order to avoid cracking the eggs. Simmer for two minutes. Remove from the heat and cover the pot for 12 minutes.
Remove the eggs from the hot water and immerse them in cold water. Peel under cold running water, and slice in half.
Pull the white part of the egg gently aware from the yolk and remove the yolks into a bowl. Mash with a fork.
Add the remaining ingredients except the microgreens and smoked trout. Stir with a fork until as smooth as possible.
Spoon the egg mixture into a piping bag fitted with a piping tip, and scrape the filling towards the tip.
Hold the bag with both hands and squeeze the filling through the tip into the cavities of the eggs.
Top with pieces of smoked trout and a sprinkle of microgreens.
Creme fraiche or sour cream can be substituted for the yogurt, or mayonnaise for more traditional deviled eggs.