Rinse the split peas thoroughly under cold water and shake dry. Place in a 4-litre Dutch oven with 2 litres cold water and bring to the boil. Simmer fast for 1 minute, removing any scum from the surface, then add all the remaining soup ingredients and bring to the boil. Reduce the heat, cover, and simmer for 1.5–2 hours or until the peas are really tender. Season to taste (you may not need to add salt, as the bacon is already quite salty). Remove the bacon from the stock and cut away and discard the rind. Shred the meat, set aside, and keep warm.
Meanwhile, make the lemon and thyme oil. Place the garlic, thyme sprigs, and lemon zest in a mortar and pestle with a little salt and pound together to release the flavors and oils. Transfer to a small saucepan, pour over the olive oil, and heat very gently for 10 minutes without allowing it to come to a boil. Set aside to cool, then strain the oil, discarding the aromatics.
Divide the soup between warm bowls and top with the shredded bacon. Drizzle over the oil and serve with a little extra thyme, lemon zest, and freshly ground black pepper, plus crusty bread alongside.