One of the nice things about modernist cuisine is being able to thicken liquids without significantly diluting the flavor of them. There are several ingredients that can do this and here I use xanthan gum to make a very flavorful balsamic vinegar syrup.
The process of making a xanthan syrup is very easy. You simply combine the xanthan gum with the liquid you want to make into a syrup at a 0.20% to 1.5% ratio by weight. It can be incorporated at almost any temperature and while it usually incorporates better if mixed with sugar first, it will not hydrate in mixtures that around more than 65% sugar.
In this case I was looking for a thick xanthan gum balsamic vinegar syrup so I went with about 1% xanthan gum by weight.
If you like this recipe you can get more than 80 other recipes from my book Modernist Cooking Made Easy: Getting Started. The book covers many of the popular modernist techniques such as gelling, spherification, and foams. It also explores modernist ingredients like agar, sodium alginate, tapioca maltodextrin, and xanthan gum. It is all presented in an easy to understand format and I think it's the best way to learn about modernist cooking.
Also, if you are just getting started experimenting with molecular gastronomy and modernist cuisine then I highly recommend one of these molecular gastronomy kits. They have everything you need to do many different dishes.
Combine all of the ingredients in a container that can hold them comfortably. Blend them together using an immersion blender until they form the xanthan gum balsamic vinegar syrup. You can easily adjust the thickness of the syrup by adding more balsamic vinegar or xanthan gum as needed.The xanthan gum balsamic vinegar syrup will last for several hours, if not days, in a useable state. When ready to serve spoon or drizzle the syrup onto your dish.