The consistency of this dish should be like hummus: thick enough to spread on bread or cling to vegetables.
Make the bouquet garni: Place the ingredients on a piece of cheesecloth. Tie into a bundle with kitchen twine.
Make the spread: Combine split peas, water, 1 teaspoon salt, and the bouquet garni in a medium saucepan. Bring to a boil. Reduce heat, and simmer until split peas are tender, about 45 minutes. Discard bouquet garni. Reserve 1/2 cup cooking liquid. Drain split peas, and let cool slightly in strainer, about 10 minutes.
Puree split peas, lemon juice, remaining teaspoon salt, and 1/4 cup plus 1 tablespoon reserved cooking liquid in a food processor until completely smooth. If the mixture is very thick, add more liquid. (Spread can be refrigerated in an airtight container for up to 1 week.)
Before serving, drizzle with oil, top with onion and capers, and season with pepper. Serve with toasts and crudites.