Add blueberries, thyme and sugar, and season lightly with salt and pepper. Cook, stirring occasionally until blueberries start to break down and thicken into a jammy consistency, about 7 to 8 minutes.
Stir in the mustard and cook another 2 minutes. Remove from heat and stir in the vinegar and lime juice. Set aside and let it cool slightly. Can be used at room temperature.