In a large bowl cover the dried cod with cold water and let soak in the refrigerator for 12 to 48 hours, (depending on the saltiness of the cod), changing the water frequently.
Bring a medium pot of water to a simmer
. Remove the salt cod from the soaking water and place in the simmering water. Poach
for 8 to 10 minutes; let cool in the liquid for another 10 to 15 minutes. Remove from poaching liquid; discard any bones and coarsely chop
Heat 2 tablespoons of the olive oil in a medium saute pan over medium-high heat. Add the garlic and shallots and cook until soft. Remove the garlic and shallots to a plate. Add the remaining 2 tablespoons of oil to the pan and lightly saute the shrimp for 1 to 2 minutes on each side. Remove the shrimp and slice in half lengthwise.
Place cream in a small saucepan
and bring to a simmer. Place the poached and chopped cod in a food processor, add shallot-garlic mixture and half of the warm cream and process until smooth. Add the pureed potatoes, remaining cream and process until just combined. With motor running add the 1/4 cup of oil. Season with salt and pepper, to taste.