Boil the potatoes: Scrub the potatoes and cut into 1-inch cubes (no need to peel Yukon Golds). Cover with cold salted water, bring to a boil, and cook until fork-tender, 15 to 20 minutes. Drain, let steam-dry for a few minutes, then mash in a large bowl.
Poach the cod: Place the cod in a saucepan, add the milk and water, and bring to a gentle simmer. Poach about 5 minutes, until opaque and flaking easily (145°F / 63°C). Remove, cool slightly, and flake into pieces, discarding any bones.
Mix: Add the cod, scallions, garlic, parsley, dill, thyme, hot pepper, red pepper flakes, salt, and a generous amount of black pepper to the potatoes. Mix well.
Shape: Scoop with a ⅓-cup measure and shape into about 16 patties. Place on a baking sheet, cover, and refrigerate for 30 minutes.
Make the aioli: While the cakes chill, stir together all the aioli ingredients. Taste, add salt only if needed, and refrigerate.
Bread: Set up three bowls: seasoned flour, beaten eggs, and breadcrumbs. Coat each patty in flour, then egg, then breadcrumbs, pressing gently.
Fry: Heat the oil in a large skillet to 350°F / 175°C. Fry 2 or 3 cakes at a time, about 2 minutes per side, until deep golden and hot in the center (165°F / 74°C). If the centers aren't hot yet, finish on a baking sheet in a 375°F oven for 5 minutes. Drain on a wire rack or paper towels.
Serve hot with the lemon caper aioli.