Place chopped anchovies on a cutting board and make a paste by dragging the side of a chef’s knife across them at a 15-degree angle about 10 times or until smooth; set aside.
Melt butter in a medium frying pan over medium heat until foaming. Add anchovy paste, onion, salt, and pepper and sauté until onion is softened but not browned, about 5 minutes.
Increase heat to medium high, add chicken livers, and sauté, stirring occasionally, until livers are browned all over, about 3 to 4 minutes.
Add Vin Santo or sherry and cook until most of the liquid has evaporated, about 2 minutes. Add chicken broth, capers, and sage and simmer, stirring occasionally, until almost all of the liquid has evaporated and the livers are cooked through, about 3 to 5 minutes.
Remove from heat, transfer livers to a cutting board, and reserve onion mixture in the pan. When cool enough to handle, finely chop the livers until they’re about the size of popcorn kernels. Return livers to the pan and stir in vinegar. Serve on toasted baguette slices.