Mix together the 1 gallon of water, kosher salt, prague powder #1, brown sugar, and picking spices in a large, sterile container. Allow salt to dissolve.
Add trimmed beef brisket to the mixture. Allow to cure for up to 10 days, turning every other day or so.
After the curing time has passed, remove brisket from brine and pat dry.
Slow Cooker Corned Beef
Place corned beef into the slow cooker and cover with water until submerged.
Add pickling spices, whole cloves, garlic, and bay leaf.
Set slow cooker to cook on LOW for 5 hours. Set a timer to add the carrots and potatoes 3 hours in.
Slice cooked corned beef very thinly against the grain. Serve with sandwiches or as a meal with the carrots and potatoes. I pureed the carrots and potatoes together with a dollop of margarine to make an Irish-inspired mash.
You could try making the pickling spices yourself, or use a pre-made seasoning as we did. We bought ours on Amazon from McCormick, linked here: