Rinse the yellow split peas under cold water until the water runs clear. Place the rinsed peas in a bowl, cover with water, and soak for at least 4 hours or overnight to reduce cooking time.

Drain the soaked peas and transfer them to a large saucepan with enough water to cover the peas by about 2 inches. Add the halved onion and bay leaf for flavor. Bring to a boil, then reduce the heat to a gentle simmer. Skim off any foam that forms on the surface.

Simmer for 1 to 1.5 hours, stirring occasionally, until the peas are soft and creamy. Add more water if needed to prevent sticking.

Remove the onion and bay leaf from the pot and stir in the butter, salt, and pepper. Use a potato masher or immersion blender to mash the peas to your desired consistency. The pudding should be thick but spreadable. Taste and adjust seasoning.

Serve the pease pudding warm or cold as a side dish or spread into a sandwich. It pairs wonderfully with gammon, ham, boiled bacon, sausages, or crusty bread.

It can also be reheated gently on the stove with a splash of water or butter to loosen the texture.