In a small bowl, stir together the yogurt, grated garlic, and ½ teaspoon salt until well combined. Set aside.
Melt the butter in a large frying pan over medium heat. Once melted, add the tomato paste and red pepper flakes and stir well. Cook, stirring often, until the tomato paste starts to stick to the bottom of the pan and the butter has taken on a red color, about 2 minutes. Transfer the tomato butter to a small bowl. Carefully wipe out the pan with a paper towel to remove the residual butter and tomato paste; there’s no need for it to be perfectly clean.
Set the wiped out frying pan over medium-high heat and add the ground beef and onions. Season with 1 ½ teaspoons salt and the pepper and cook, breaking up the meat with a spatula and stirring it often, until the beef is no longer pink and becoming crispy, about 10 minutes.
While the beef is cooking, bring a large, covered pot of water to a boil over high heat. Once the water is boiling, season with plenty of salt and cook the pasta to al dente according to the package instructions. Drain well in a colander or sieve.
Portion the pasta onto serving plates. Top each portion equally with the yogurt sauce, beef, and a generous drizzle of the tomato butter. Sprinkle with plenty of the chopped parsley and serve immediately.
