Preheat the oven to 350 degrees F and preheat a grill to high.
Place the potatoes on a baking sheet, drizzle with canola oil and season with salt and pepper. Roast until tender and slightly browned, 20 minutes. Transfer the potatoes to a medium bowl and mash until smooth. Cover and set aside.
Meanwhile, brush the sourdough slices on both sides with olive oil. Grill until toasted and slightly charred on both sides, about 2 minutes per side. Remove the bread from the grill and halve diagonally. Set side.
Set a medium, high-sided saute pan over medium-high heat. Add 2 tablespoons olive oil and the salt cod and saute for 30 seconds. Add the roasted garlic, thyme and heavy cream, and sprinkle with white pepper. Bring to a boil, then immediately lower to a simmer. Cook until the cod has softened and is cooked through, 15 to 18 minutes. Remove the thyme bundle and flake the cod with a fork until shredded. Add the mashed potatoes, lemon juice, and zest, and cream together to make a spread.
Drizzle the brandade with olive oil and garnish with parsley. Serve with the grilled sourdough.
Preheat the oven to 425 degrees F.
Slice the top off of the head of garlic, just enough to expose the cloves. Set the garlic on a piece of aluminum foil, drizzle with olive oil and sprinkle with salt and pepper. Wrap up the foil into a tight pouch and roast for 35 to 45 minutes.