Fill large pot or other large, heat-resistant container with water. Insert sous vide immersion circulator and set to 155° Fahrenheit. Note: pot must be deep enough that water level falls between minimum and maximum indicators on circulator.
Add ¼ cup salt, 2 packed tablespoons brown sugar, 1 tablespoon paprika, ½ tablespoon garlic powder, ½ tablespoon onion powder, 1 teaspoon dry mustard, 1 tablespoon dried thyme, and ½ teaspoon cayenne pepper to small bowl. Whisk until spices are well incorporated.
Place whole brisket on cutting board. Sprinkle approximately two-thirds of spice mixture over all sides of brisket and gently rub mixture into brisket. Reserve remaining spice mixture for later in recipe.
Transfer dry-rubbed brisket to food-safe bag. Remove as much air from bag as possible with vacuum sealer or water displacement method (see Notes) and seal bag shut.
Once water bath is preheated to 155° Fahrenheit, place sealed bag in pot, making sure brisket is fully submerged. Weigh bag down with weights or silverware attached to bottom of bag if needed. Food must be fully submerged to cook properly.
Cook brisket in water bath 24 to 36 hours, until desired texture is achieved. Note: brisket will be fully cooked after 24 hours but is safe to continue cooking up to 36 hours. Longer cook time will yield more tender meat.
Toward end of cook time, preheat oven to 300° Fahrenheit. Move oven rack to lower-middle position.
When brisket is cooked as desired, carefully remove bag from water bath. Remove brisket from food-safe bag and pat brisket completely dry with paper towels. Sprinkle remaining dry rub mixture over all sides of brisket.
Transfer seasoned brisket to baking pan. Place pan in preheated oven and cook, uncovered, 2 hours or until dark bark has formed on top of brisket.
When bark has formed, carefully remove brisket from oven. Transfer brisket to cutting board and cover brisket loosely with aluminum foil. Let brisket rest, covered, 30 minutes, then slice brisket against grain and serve with desired sides.