Finely grate the garlic using a microplane. Alternatively, you could grind the garlic into a fine paste in a mortar and pestle OR use a knife to finely mince the garlic and use the side of the knife to "smear" the garlic into a fine paste.
Add the olive oil to the garlic and set aside.
Cut the peeled potatoes into 1/2 inch slices and place in a bowl of water to rinse off excess starch. Let them sit for a minute or two.
Remove the sliced potatoes from the water and place in a pot with the bay leaf and enough milk to cover them.
Drain the salt cod from the soaking water and place into a separate pot with enough milk to cover the cod.
Bring both pots up to a gentle simmer over medium-low heat and allow them to simmer. The salt cod will simmer for 10 minutes and the potatoes will cook for about 10-15 minutes, or until they are tender when pierced with a knife.
After simmering for 10 minutes, strain the cod and reserve the hot milk. ***If the potatoes are done cooking at this point, just turn off the heat and let them sit in the hot milk until you are done processing the salt cod. You don't want the potatoes to cook to the point of completely falling apart and dissolving into the milk.***
Place the drained cod in a bowl and spread it out so it cools quickly. You can put the bowl in the fridge for a minute or two to speed this up.
Once cool enough to handle, break the cod into small pieces by rubbing and squeezing it with your (clean) hands. If there were any bits of skin, bone, silverskin, or bloodline, now is the time to remove them.
The cod should be finely broken up and resemble threads. Set the cod aside.
When the potatoes are tender, strain them from the hot milk and discard the bay leaf. Reserve the hot milk and combine it with the milk that was used to cook the cod.
You have a few options for processing the potatoes. You can either pass them through a potato ricer, pass them through a tamis, or just crush them with a fork until relatively smooth. Here I am crushing them with a fork. Whichever method you choose, make sure you process the potatoes while they are still hot so that they do not get gummy.
**OPTIONAL STEP** If you crushed the potatoes with a fork, you can then press the potatoes through a medium-fine meshed strainer with a rubber spatula to work out any lumps. This step is optional but will yield a smoother brandade. Again, make sure you do this while the potatoes are hot.
Combine the warm potatoes and cod in a mixing bowl.
Measure out 4 oz (120 grams) of the reserved cooking milk and discard the rest. Add the 4oz milk, the garlic/olive oil mixture, and the picked thyme leaves to the bowl with the cod and potatoes. Mix everything together. The brandade should resemble the texture of mashed potatoes. Taste the brandade and add salt as necessary. The amount of salt necessary will vary depending on the salinity of your salt cod. It should be seasoned well... slightly saltier than normal mashed potatoes.
At this stage you can store the brandade in the fridge for up to 3 days.
When you are ready to serve, spread the brandade in the bottom of an oven-safe serving dish, ramekin or skillet. Don't spread the brandade in a layer any thicker than 1 inch. In this photo, I only used about half of the brandade that I made and saved the rest for later.
Place the brandade under the broiler and cook for about 5 minutes or until the brandade is warm and golden on top. **see note below regarding cooking time**
Drizzle the brandade with a little more olive oil if desired and serve with grilled/griddled bread.