Heat oven to 400°F. In 5-quart saucepan, heat 1 tablespoon butter over medium-high heat. Add half the beef cubes; cook until browned on all sides, about 3 minutes. With slotted spoon, remove beef to medium-size bowl. Add 1 tablespoon butter to saucepan; add remaining beef cubes and brown as above; remove the beef to the bowl.
In same saucepan, heat remaining 2 tablespoons butter. Add onions and mushrooms; sauté 5 minutes. Add baby carrots.
In small bowl, stir together beef broth and flour until smooth. Stir into vegetable mixture in saucepan along with wine, thyme, salt, pepper and tomato paste. Bring to boiling; lower heat and simmer, stirring occasionally, until thickened, about 2 minutes. Return beef cubes with accumulated juices to saucepan. Spoon into shallow 3-quart round, oval or rectangular casserole.
On lightly floured surface, unfold puff pastry sheet. With fingers, press pastry to flatten fold creases. With 3-inch oval or round cookie or biscuit cutter, cut a hole in center of puff pastry sheet. Place pastry sheet at an angle on top of beef burgundy in casserole so it creates a diamond pattern. Trim overhanging pastry to edge of casserole.
Bake in 400°F oven for 20 minutes or until pastry is golden and puffed and casserole is bubbly. Let stand 10 minutes before serving.