Vanilla bean paste is an alternative to vanilla extract that contains vanilla seeds and specks of beans... it makes vanilla custards, ice creams, créme brûlée, etc. a little prettier. You can sub it teaspoon-for-teaspoon with vanilla extract.
5 vanilla beans (if old/dry, can still use, but maybe add a couple more)
1/4 c vanilla extract
1.5 T light corn syrup
1/2 c sugar
1/2 c water
xanthan gum
glycerin
Scrape seeds out of vanilla beans and mix with vanilla extract in a small jar. Set aside.
Chop beans roughly in 1/2" pieces and dry until they are brittle, or nearly so. This can be done by leaving them out for a few days (in a dry climate) or in a VERY low oven, tossing/checking often. (I dried for a day on the counter, got impatient, then moved to the toaster oven to finish them off... as low as it went, tossing every 3-4 minutes, they were good to go in about 10 minutes. NOTE: they will get more brittle as they cool - so you may want to leave a couple pieces out after each tossing to see how they're really doing.
Put beans in a CLEAN coffee grinder and whir to a powder.
Mix corn syrup, sugar, and water in a small saucepan. Heat until sugar dissolves and simmer 5 minutes. Remove from heat. Allow to cool briefly and add vanilla bean powder and extract with seeds. At this point it is done by most recipes I found.
BONUS STEP: The paste I've bought at Trader Joe's is much thicker and when I checked the ingredients list, found it contains xantham gum, a powerful thickener that does not require heat. I've used it before and found it really challenging to NOT end up with lumps (since you don't have significant time to break up any tiny clumps of it that land on a liquid surface. Most advice suggests putting the liquid to be thickened in a blender and dusting the xanthan gum powder into the vortex through a fine mesh strainer. But that's not practical in this case. However, changed my search terms, and came up with a genius suggestion that works perfectly here... mix your xanthan gum with a bit of food-grade glycerin. Once it's well-mixed with no tiny clumps, add it to the vanilla bean paste until you're happy with the thickness. I mixed probably 1/2 t xanthan gum powder with 1-1.5 t glycerin, then added some to plain water (to see if it really worked)... then whisked a little bit at a time to the vanilla bean paste. It was a lot of by-guess and by-gosh - I maaaaybe ended up with about half the total xanthan/glycerin mix in my paste. It'll be quite awhile til I make more, but will try to get better measures then.