At this point, start incorporating the olive oil a scant teaspoonful at a time, alternating with drops of milk without ever ceasing to stir rapidly; the brandade gains in fine texture through rapid stirring.
If it becomes too thick, add more oil and milk.
Complete the seasoning by adding a few drops of lemon juice and white pepper. A brandade should have the consistency of mashed potatoes (which it looks like).
Fry the slices of bread in the hot oil until golden brown, about 1 to 2 minutes.
Remove and drain on paper towels.
Season with salt and pepper. Serve the brandade with the fried bread.