Preheat the oven to 200°C (390°F). In a frying pan over medium heat, sauté the onions and garlic until translucent.
Add the minced beef to the pan and cook until browned, breaking it apart with a spatula. Drain any excess fat.
Mix in the diced carrots, tomato paste, Worcestershire sauce, mild paprika, thyme, salt, and pepper, cooking for an additional 5 minutes. Remove from heat and let the filling cool slightly.
Roll out half the puff pastry and line the pie dish. Fill with the beef mixture, then cover with the remaining pastry, sealing the edges. Cut slits in the top for steam to escape.
Brush the top with the beaten egg for a golden finish.
Bake in the preheated oven for 25-30 minutes, or until the pastry is golden brown and puffed.
Allow the pie to rest for about 10 minutes before slicing. This helps the filling set.
In a mixing bowl, toss the mixed greens, cucumber, and cherry tomatoes with olive oil, balsamic vinegar, salt, and pepper.
Serve slices of the meat pie alongside the fresh salad.
