MAKE COOKIE DOUGH:
In large bowl, whisk together flour, baking soda, & salt; set aside. In second large bowl, with an electric mixer, cream the sour cream and butter at low speed; add sugar, eggs, and vanilla & mix until combined. (It's okay if it's a little lumpy as long as no butter chunks are visible.) Gradually add the flour mixture to the sour cream mixture, mixing until well combined. Dough will be sticky. (If cookie dough is too thick for your mixture to handle, you can stir it by hand with a wooden spoon.) Divide dough onto two pieces of plastic wrap; flatten dough, wrap tightly, and refrigerate until chilled, 1-2 hours. (Make ahead tip: Dough may be made to this point and refrigerated for up to 3 days or frozen for up to 1 month.)
ROLL, CUT, & BAKE COOKIES:
Preheat oven to 350 degrees. Line 2 baking sheets with parchment paper; set aside. Generously flour your counter or work surface to prevent dough from sticking. Rub flour on the rolling pin. Put one of the chilled pieces of dough on top of the floured surface and sprinkle the top of the dough with more flour. Starting at the center, roll the dough out to one edge; return to the center and roll to the opposite edge. Continue rolling until dough is an even 1/4" thick all over, sprinkling with additional flour, if needed, to avoid sticking. Dip cookie cutter in flour and cut out dough shapes. Transfer dough shapes to baking sheets. Continue rolling dough, cutting shapes, and adding to baking sheets until they are filled. Bake 2 sheets at a time for 8-10 minutes, rotating and switching pans half way through cooking time. Bake them just until they are baked all the way through but haven't started browning on the bottom. If a soft textured cookie is desired, it's very important not to over bake them. Transfer hot cookies to a baking rack to cool completely.