In a large nonstick pan over medium high heat, brown ground chuck, onions, and garlic together until the meat is no longer pink. About 7-8 minutes.
Add salt and pepper.
Turn heat down to medium, add butter. Stir until melted. Add flour. Cook and stir for 2-3 minutes.
Slowly add beef stock. Stir until mixture has thickened slightly and heated through.
Stir in fresh dill. Transfer to covered container. Place in fridge. Chill completely.
Meat Buns
In a dry pan, toast the caraway seeds over medium high heat until fragrant, careful not to burn. About 2 minutes. Transfer to a small bowl to cool.
In small saucepan heat butter and milk together until it reaches about 120°F (50 °C) on thermometer. Stir to cool down if too hot. (If too hot it will kill the yeast).
Add milk mixture to bowl of a mixer, fitted with dough hook attachment. Add yeast. Stir to dissolve.
Whisk in egg yolks.
In separate bowl, whisk together flour, sugar, salt, and toasted caraway seeds. Add to wet mixture.
With mixer on medium speed, knead dough for approximately 7-8 minutes until a smooth ball forms.
Remove from bowl. Transfer to a large, greased mixing bowl. Cover. Allow dough to rise for about 1-1½ hours until doubled in size.
Once dough has risen, punch down. Divide into ~30 portions (30g each). Cover with a towel to prevent dough from drying out.
Grease a 13-inch x 9-inch pan (33 cm x 23 cm) with butter along bottom and sides.
With a rolling pin, roll each portion out to form a round of about 4-4½ inches (10-11.25 cm) in diameter. With the round in the palm of your hand, spoon about 1 tablespoon of meat filling into centre and gather edges. Pinch firmly to create a seam.
Place pinched buns, seam side down, in prepared pan. Once the pan is filled, cover with a towel. Allow to rise another 30-60 minutes or until they have increased 50% in size.
In small bowl make an egg wash by whisking together 1 egg and water until smooth and there are no streaks of egg white. Brush buns with egg wash. Top with a pinch of extra toasted caraway seeds.
Bake at 375°F (190°C) for 20-25 minutes until golden brown.
Remove from oven. Immediately generously brush with melted butter.