Roast the garlic - see notes.
Meanwhile, combine undrained cannelini beans and drained chickpeas in a pot with enough water to cover them by at least 1 inch.
Bring to a boil to soften the beans.
Reserve 1/2 cup of the water and then drain the beans.
Add the beans to the food processor along with the 1/2 cup of bean water.
Blend until smooth.
Add roasted garlic and grated raw garlic; blend until smooth.
While blending, slowly add 1 tbsp of olive oil.
Add tahini; blend.
Taste for salt and olive oil; adjust accordingly.
Blend for at least 5 minutes or until you've reached your desired smoothness.
Garnish with olive oil and paprika, if desired.
Store in an airtight container for up to 4 days.