In a small saucepan, combine the cranberries, thyme, and ¾ cup and 2 tablespoons of water. Bring to a boil, then reduce the heat to medium-low and simmer for 3 minutes, stirring occasionally.
Add the sugar, mustard, vinegar, lemon juice, salt, and pepper. Continue to simmer for 3 to 5 minutes, stirring regularly.
In a small bowl, combine the remaining water with the cornstarch, then add to the saucepan. Cook for 1 to 2 minutes, stirring, until the mostarda thickens.
Transfer to a covered, food-safe container and refrigerate for up to one month.
Tip: Next time you make turkey burgers, spread one side of the bun with cranberry mostarda.