Combine the mayonnaise and chiles in a small food processor or blender and process until smooth. Add a little water if needed so the mixture runs smoothly through the blades. Transfer the chipotle mayonnaise to a small bowl.
Remove the center third of each leek and save to use in a soup or salad. Cut the large outer pieces crosswise into ¼-inch slices. Lay the slices of leek on one side of a piece of parchment paper and fold the empty side over so that the leeks are covered by parchment. Microwave at 40% power for about 12 minutes, stirring every 3 minutes, until the leeks are dry and crispy.
In a medium bowl, whisk together the soy sauce, lime juice and orange juice. Add the tuna to the bowl and let it marinate for 2 minutes. Transfer the tuna to a plate.
To assemble the tostadas, spread about 1 ½ teaspoons chipotle mayo over each tostada. Top each with about 3 slices of tuna, a slice of avocado and a sprinkling of dried leeks.