Preheat the oven to 375°F.
Lay out the phyllo pastry sheets on a clean surface. Brush each sheet lightly with melted butter and stack them on top of each other.
Cut the stacked phyllo into squares (about 4 inches each) and place them on a baking sheet lined with parchment paper.
Bake the phyllo squares for 10-12 minutes or until golden brown and crispy. Remove from the oven and let cool.
While the phyllo is baking, bring a small pot of water to a simmer. Carefully crack the eggs into the simmering water and poach for about 3-4 minutes, or until the whites are set but the yolks are still runny.
Remove the eggs with a slotted spoon and place them on a paper towel to drain.
In a small bowl, mix the cream cheese, dill, capers, lemon juice, salt, and pepper until well combined.
To assemble, layer a phyllo square on a plate, spread a thin layer of the cream cheese mixture, add a slice of smoked salmon, and top with a poached egg.
Repeat the layers, finishing with another phyllo square on top. Garnish with avocado slices and microgreens if desired.
Serve immediately while the phyllo is crispy.