In the blender, purée together all the ingredients, except for the last two.
Transfer the mixture to a saucepan and bring to a boil over medium-high heat. Lower the heat to medium and simmer until the mixture thickens up a bit and the garlic-pepper bits begin to soften, about 3 minutes.
Combine the cornstarch and water to make a slurry. Whisk in the cornstarch mixture and continue to simmer one more minute. The cornstarch will help the sauce to thicken slightly thereby causing nice suspension of the garlic-pepper bits; otherwise, you get a thin sauce with all the little pieces floating on the surface.
I keep the chili seeds in, but your mileage may vary, so adjust the heat accordingly. More seeds = more heat. Keep in mind, however, that the heat is the strongest the day you make the sauce and starts to dissipate gradually. This sauce keeps for a long time, and after a couple of weeks, you can’t even taste the pepper.
If you want to make a large batch of this sauce (more than half a gallon) — and you certainly should since this sauce lasts a long time — the best thickener to use is pre-gelatinized or “pre-gel” starch which is both acid- and heat-stable (corn or potato starch is not). It’s marketed under the brand name Clearjel®. Your chilli sauce will remain viscous and maintain the nice suspension for the entire duration of its shelf life when thickened with pre-gelatinized starch.