1. Measure mustard into a small bowl. (Ground mustard has a tendency to clump so you may have to pass it through a sieve.) Add brown sugar, paprika, turmeric, and salt. Whisk together, making sure there are no lumps, and set aside.
2. Combine the unheated water and vinegar in a mixing bowl. Add combined dry ingredients and whisk until smooth.
3. Pour mustard mixture into a heavy saucepan and heat on medium until it just begins to simmer.
4. While the mixture is coming to a simmer, make a slurry by measuring very hot water into a mixing cup and adding the cornstarch. Whisk until completely smooth.
5. When the mustard mixture begins to simmer, add the slurry and whisk. Scrape to make sure nothing is congealing along the sides or bottom. Increase heat to reach a slow boil, then cook for about a minute, stirring continuously. Remove from heat and let stand just until cool enough to transfer to a lidded jar. Store in the refrigerator.