Combine olive oil, parsley, capers, Dijon, mustard, lemon juice and anchovies.
Slice baguette into 20 thin slices and 8 bocconcini cheese balls into 16 halves. Threads 5 slices of bread and 4 pieces of cheese on each skewer, alternating each, beginning and ending with bread.
Grill skewer, turning often, until bread is toasted and cheese begins to melt, 4-5 minutes. Remove from grill; drizzle with anchovy sauce.