Stir butter and garlic in stockpot over medium heat until butter begins to brown. Remove garlic and discard.
Stir shallots into browned butter. Cook and stir until translucent, 5 to 7 minutes.
Pour sherry over shallots in the stockpot and bring to a boil while scraping any browned bits off of the bottom of the pot. Simmer until liquid is reduced by half, 3 to 5 minutes.
Pour reserved oyster liquor, milk, and cream into the stockpot; bring mixture to a simmer. Reduce heat to medium-low and stir in oysters; cook until oyster edges begin to ruffle, about 3 minutes. Remove from heat.
Stir in parsley; season with sea salt to taste. Ladle into bowls and garnish with sweet paprika and oyster crackers.
