Preheat oven to 425 degrees or 400 degrees for convection.
With a sharp knife, cut pastry sheet horizontally and vertically down the middle, creating 4 equal squares. Fold each square into a triangle. Make a cut 1/2” into the triangle along the open sides, not the folded base, leaving all pieces intact.
Beat 1 egg. Unfold the triangle, brush the edges of the inside square with egg and fold one cut corner over the opposite inner corner. Repeat with the other corner, overlapping the first, placing on the opposite inner corner.
Brush the top with beaten egg and prick the inner square with a fork 4 times. Repeat with the remaining squares. Place on a parchment-lined baking sheet and bake 10 min, then rotate and bake 4 min. Remove from oven and set aside. Lower oven temperature to 375° or 350° for convection.
Meanwhile, make filling by browning sausage in a skillet, breaking into small pieces. Drain on paper towels. In same pan over high heat, sauté tomatoes 20 sec until skin blisters. Toss with 1 T parsley and 1 T chives (reserve remainder for garnish). Remove from heat.
Using a sharp knifepoint, gently cut around edges of the top layers of inner square, pressing down (do not cut all the way through to bottom) to create a ‘box’. Into each, break 1 egg. Divide sausage, tomatoes and cheese between them. Sprinkle with salt and pepper. Brush edges with egg and bake 8 min.; rotate and bake 5 min. more, until egg white sets. Garnish with remaining parsley and chives. Serve warm.
* Thaw puff pastry in the fridge overnight. Unfold and press to mend any breaks or tears in the seam.