Boil the eggs: Place the eggs in a medium pot and cover them with cold water. Bring the water to a boil over medium heat. Once boiling, reduce the heat to low and simmer for 9-12 minutes. Afterward, transfer the eggs to a bowl of ice water to cool completely.
Prepare the filling: Once the eggs are cool, peel them and cut them in half lengthwise. Carefully scoop out the yolks into a bowl. Mash the yolks with a fork, then mix in mayonnaise, Dijon mustard (if using), salt, and pepper until smooth. Add in the finely chopped strawberries or strawberry puree and stir to combine.
Fill the eggs: Spoon the strawberry yolk mixture back into the egg white halves, or for a neater presentation, use a piping bag or a plastic sandwich bag with the corner snipped off to pipe the mixture.
Garnish and serve: Top each deviled egg with a slice of fresh strawberry. For added flavor and a gourmet touch, drizzle with a bit of balsamic glaze. Serve chilled.