To make the filling: Heat a large skillet over medium-high heat. Cook and stir ground beef in the hot skillet until browned and crumbly, 5 to 7 minutes; drain. Stir in onion; cook and stir until onion has softened. Season with salt, pepper, and dill weed to taste. Allow to cool before using.

Meanwhile, to make the dough: Dissolve yeast in warm water and place in a warm location until frothy, about 10 to 15 minutes. Warm milk in a medium saucepan over low heat; gently whisk in eggs, oil, sugar, and salt. Remove from heat.

Place 1/2 of the flour in a large mixing bowl and gradually stir in the milk mixture. Add yeast solution alternately with remaining flour, stirring after each addition; mix well. Knead until the dough forms a ball and does not stick to the bowl. (Note: Start with the 4 cups of flour. You may need to add more, a little at a time, as you knead the dough). Cover the bowl with a clean cloth. Set in a warm location and allow to rise until doubled in volume, about 30 to 60 minutes.

Remove dough from bowl and place on a lightly floured surface. Pinch off pieces approximately the size of golf balls. Roll the pieces into disks about 3 1/2 to 4 inches in diameter.

Fill the center of each disk with a heaping tablespoon of cooled beef mixture. Fold disks over the mixture and firmly pinch the edges to seal. Arrange on a flat surface and allow to sit for approximately 10 minutes.

Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C). Lower piroshki carefully into the hot oil in batches. Fry until golden brown on one side, about 3 to 4 minutes; gently turn and fry the other side. Transfer to a paper towel-lined plate to drain. Repeat with remaining piroshki.