Beef Stroganoff with Buttered Noodles

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4 cloves garlic, roughly chopped, plus 2 cloves, minced

Kosher salt and freshly ground black pepper

Extra-virgin olive oil

1 sprig fresh rosemary, leaves removed

1 large sprig fresh thyme, leaves removed

3 pounds beef short ribs, cut into 2 ribs apiece

1 1/2 pounds cremini mushrooms

1 1/2 pounds white button mushrooms

1/2 cup chopped shallots

1/4 cup cognac

2 cups heavy whipping cream

1 tablespoon Dijon mustard

1/2 cup sour cream

1 pound egg noodles

3 tablespoons unsalted butter

2 tablespoons freshly chopped flat-leaf parsley

2 tablespoons freshly chopped green onions