Whisk milk, 1 cup plus 3 tablespoons flour, eggs, and sugar together in a bowl. Add 1/4 cup melted butter; whisk well. Let batter sit, 15 to 20 minutes.
Bring a pot of water to a boil. Add beef; cook until no longer pink, 5 to 7 minutes. Drain. Chop the boiled beef finely until even in texture.
Heat 2 tablespoons butter in a skillet over medium-low heat. Add onion and cook, while stirring, until soft and golden, about 10 minutes. Increase heat to medium and add the chopped beef, salt, and pepper. Cook and stir filling until flavors combine, about 10 minutes.
Heat oil in a nonstick or cast-iron skillet over medium heat. Pour 3 to 4 tablespoons of batter into the skillet and quickly rotate the skillet to spread batter out in a thin layer. Cook until edges are brown, 1 to 2 minutes. Run a spatula around the edge of the skillet to loosen blini; flip and cook until the other side has turned light brown, about 1 minute more. Repeat with remaining batter.
Spread 2 tablespoons beef filling on 1 side of each blini. Fold edges over filling and roll blini up. Repeat with remaining filling and blini.
Use any beef you prefer, including pre-boiled beef from the store.
Instead of chopping the beef you can run it through a meat grinder.
You can also pan fry the rolled blini at the end in a bit of oil for even more flavor.
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