Using food-safe kitchen scissors, cut the beans into 1-inch pieces directly into the blender container. A knife and cutting board also work, but the beans can leave a sticky residue on the board.
Add the vodka, sugar, and corn syrup.
Secure the lid and blend on low for about 30 seconds, until the beans begin to break down. Gradually increase the speed to high and blend for about 2-3 minutes, until the beans are finely processed. The paste will warm up as it blends, which helps everything come together.
The finished paste should be smooth, slightly thick but pourable, and speckled with fine flecks of vanilla bean. The paste will thicken some as it sits.
Let the paste cool, then transfer it to a clean glass jar with a tight-fitting lid.
Your vanilla paste is ready to use in baking right away. I like to let mine rest for 1 month before using it, which gives the flavor time to develop and the alcohol taste time to mellow. If you plan to use it in drinks, whipped cream, or anything that isn't cooked, wait at least 2 weeks.