Place the split peas, water, baking soda and ½ teaspoon of salt in a medium saucepan. Bring to a boil over high heat, and then reduce the heat to low. Simmer, stirring occasionally, until split peas are very tender and falling apart, about 30-45 minutes. If the peas are starting to look a little dry, add a little more water to the pan to keep the mixture from sticking to the bottom of the pan. Set aside to cool slightly, about 10-15 minutes.
Transfer the minced garlic and lemon juice to the work bowl of a food processor or to a blender. Let the garlic sit in the lemon juice for about 10 minutes (this will help mellow the flavor of the raw garlic).
Transfer the cooked split pea mixture (no need to drain) to the food processor along with the cumin and tahini paste. Process until smooth. With the food processor running, slowly add the olive oil through the feed tube. Season with additional salt to taste.
Scrape the hummus into a bowl and cover with plastic wrap. Store in the refrigerator until completely cool. When you are ready to serve, give the hummus a stir to fluff it up a bit and drizzle a little olive oil over the top.