To make the mayonnaise, beat the egg yolks in a medium bowl with an electric mixer or hand blender. Slowly blend in the oil, one tablespoon at a time while mixing constantly. Continue to add oil until the consistency is a little thicker than regular mayonnaise. Pierce the garlic clove and stir it around in the mixture until it releases its juice. Remove the garlic and season with salt and pepper. Mix in the red wine vinegar 1 teaspoon at a time. Go slow, this will thin the mayonnaise a bit.
Place the eggs in a large saucepan with enough water to cover. Bring to the boil, then simmer for 10 minutes. Remove from the heat, drain and cool. Peel off the shells and cut eggs in half lengthways. Remove the yolks and place them into a medium bowl. Place the egg whites on a serving plate.
To the yolks, add shallot, salmon, 125ml of the mayonnaise, salt and pepper. Mix until well blended. If the mixture seems dry, stir in more mayonnaise. Spoon or pipe into the egg white halves and chill or serve.