Heat the oven to 425°F.
Roll the puff pastry as little as possible to smooth out any creases. Trim the edges to create a sharp rectangle and place the pastry on a large baking sheet.
Using a knife, score the pastry to create a 1-inch frame around it. Using a fork, poke the pastry all over avoiding the 1-inch thick frame.
To a small bowl, add one egg and one tablespoon of water. Whisk vigorously to combine. Using a brush, brush the egg wash on the 1-inch frame.
Bake the pastry for 15 minutes, until lightly golden and puffed.
Remove the pastry from the oven. Using a flat-bottomed measuring cup, flatted and press down the poked pastry (avoiding the 1-inch frame).
Brush with another layer of egg wash and bake for 10 to 15 minutes, until golden brown all over.
Cool the pastry to room temperature.
Meanwhile, in a food processor, add the cream cheese, ricotta and pulse for a 2 to 3 minute, until whipped.
Add the chives, dill and quickly pulse until incorporated. Season with salt.
Spread ⅔ of the cheese mixture on the pastry. Add the remaining ⅓ to a piping bag. Pipe 6 rings on the pastry.
Poach the eggs: bring a large pot of water to a boil. Reduce the heat to medium-low, to a steady simmer.
Place a mesh strainer over a large bowl. Crack the remaining 6 eggs in the mesh strainer.
Using a spoon, stir the water to create a vortex. Dump all the eggs in the vortex.
Poach for 2 to 3 minutes, until the egg whites are opaque but the yolks are wobbly.
Using a slotted spoon, place each egg in its nest. Season with salt and pepper.
