Dice sirloin into bit sized pieces, season with salt and pepper. Toss with flour to coat.
Heat oil in a Dutch oven over medium high heat. Add sirloin and saute until browned.
Add onion and cook for 1 additional minute.
Add celery, carrots, and herbs. Cook for an additional 5 minutes.
Pour in the Guinness. Scrape bottom of pan to remove the browned bits that stick to the bottom.
Add the tomatoes and bring to a boil, stirring occasionally. Reduce heat and simmer for 2 hours, or until the meat is tender. Sauce should become nice and thick.
Preheat oven to 375 degrees.
Scoop filling into 4 to 6 porcelain bowls/ramekins or one large casserole dish.
Roll out puff pastry and cut out circles slightly larger than the size of the dish/dishes.
Brush the rim of the dish/dishes with beaten egg, then place pastry on top of dish. Smooth the pastry along the edges of the dish to secure. Cut steam vents in the pastry and brush with remaining egg wash.
Place dish/dishes on a baking sheet and bake on the center rack of a preheated oven and bake for 25 minutes (individual dishes), 35 - 45 minutes (large casserole), or until pastry is puffed and golden brown.
Remove from oven and let sit for 10 - 15 minutes before serving.
Notes
To make the puff pastry shamrock cut-outs. Place them on a separate baking sheet, brush with egg wash {I sometimes dye it green} and bake them for 8 to 10 minutes.
I used (5) 4.25 inch by 2-inch ramekins that hold 8 ounces each.
Each oven cooks differently so be aware and keep an eye on your pies.