Slice vanilla beans in half lengthwise. Using tip of paring knife, carefully scrape out seeds and transfer to small saucepan. Cut bean pods into 1" pieces and add to saucepan. Cover the saucepan.
Add vodka, cover, and cook over medium-low heat until mixture is hot and steaming, but not boiling, about 3 minutes. (Do not open lid while pot is over flame or alcohol will ignite.)
Pour mixture into jar with tight-fitting lid and let cool to room temperature. Cover with lid and store in dark place for at least 6 weeks (or up to 10 weeks for a stronger vanilla). The seeds and pods will settle so shake jar gently once a week or so.
Feel free to taste the vanilla mixture at 6 weeks. If it's not strong enough, close the lid and let it sit longer. Once you remove the pods and seeds, the vanilla extract stays at that strength.
Line fine-mesh strainer with 2 coffee filters and set over liquid measuring cup. Strain vanilla through filters and transfer liquid to a clean jar with tight-fitting lid.
Vanilla extract will keep in the pantry indefinitely.