For the mayonnaise: Whisk together the egg yolk, lemon juice, vinegar, and salt in medium bowl. Whisk rapidly until well-combined (about 45 seconds).
Very slowly drizzle in the olive oil, a little at a time, whisking as you go. Then gradually and slowly drizzle in the 1/2 cup of canola oil, whisking constantly (you can use a food processor for this if you prefer), until the mayonnaise thickens.
Whisk the finely chopped basil into the mayo (I often blend it with a blender or food processor quickly), then refrigerate for at least 1 hour to let the flavors mellow together.
For the sandwich: Spread the bread thickly with the basil mayonnaise, and layer on the remaining ingredients, dividing them evenly between both sandwiches. Adjust to your taste!