Return the skillet to medium heat and add the onions and cook for about 7 minutes until they begin to turn light golden brown. Add the garlic and cook for 45 seconds until fragrant. Season with salt, pepper, crushed red pepper, and 1-2 shakes of smoked paprika.
Add the tomato paste to the skillet and coat the onions and garlic completely in the paste. Cook, stirring often, until the paste begins to deepen in color, about 5-6 minutes. Turn the heat to medium high and cook an additional minute or two.
Deglaze the pot with the vodka, scraping up any browned bits stuck to the bottom. Continue stirring the vodka into the sauce until smooth and completely incorporated. Pour in the crushed tomatoes and the reserved cooked beef and then reduce heat and simmer for 15 minutes. Taste and season with salt, pepper, a bit more crushed red pepper and sugar if desired.