Drain the beans, discarding the water, and place them in a large pot.
Pour the stock over the beans and bring to a boil. Add half the butter and boil about 5 to 7 minutes, covered. Add the water and shallot and return to a boil. Lower the heat and simmer for 60 minutes. Add the remaining butter and salt and pepper. Cook another hour until the beans are tender.
Cover beans with cold water and soak overnight. Drain beans and place them in a saucepan, cover with cold water. Bring to a boil and reduce the heat to a simmer, and simmer until tender (about 45 minutes). Drain and cool.
In a food processor, chop garlic and the jalapeno. Add beans and with the motor running, process while slowly adding the water and oil through a feed tube. Add remaining ingredients and process until smooth. Adjust seasoning if necessary.