1. Open the can of marrowfat peas and drain them through a strainer, rinsing briefly under cold water. Measure out 1/3 cup (about 65 g) of whole peas and set aside. Place the remaining peas in a medium heavy saucepan (3–4 qt / 2.8–3.8 L).
2. Add 1 cup (240 ml) cold water, the onion half, bay leaf, parsley sprig, blade of mace, sugar, salt, and pepper to the saucepan. Bring to a gentle simmer over medium-low heat — small bubbles breaking the surface — then reduce heat to low and simmer uncovered for 30 minutes, until the peas are very soft and have lost their shape when pressed against the side of the pot.
3. Remove and discard the onion, bay leaf, parsley, and mace. Pass the pea mixture through a fine-mesh sieve or food mill into a clean saucepan, pressing firmly to extract all pulp. Discard the solids remaining in the sieve. Stir in the 3 cups (720 ml) White Stock. Set over low heat.
4. In a small saucepan over medium-low heat, melt the butter completely (technique: beurre manié / roux base — a fat-and-starch mixture used to thicken without lumps). Add the cornstarch all at once and stir continuously with a wooden spoon for 1–2 minutes, until the paste is pale golden, smells faintly nutty, and pulls away slightly from the sides of the pan. Do not allow it to brown.
5. Whisk the butter-cornstarch paste gradually into the warm pea-and-stock mixture, a small spoonful at a time, stirring constantly to prevent lumps. Bring the soup to a full boil over medium heat — large, steady bubbles — and cook for 5 minutes, stirring frequently, until the soup is thickened enough to lightly coat the back of a spoon.
6. Reduce heat to low. Stir in the 1 cup (240 ml) whole milk and the reserved whole peas. Heat gently for 3–5 minutes, until steaming throughout and the reserved peas are warmed through. Do not boil after adding the milk. Taste and adjust seasoning. Serve immediately.
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