In a medium saucepan of boiling salted water, cook the leeks over moderately high heat until tender when pierced with a knife, about 12 minutes for medium leeks and 8 minutes for small ones. Refresh the leeks in a bowl of cold water for 1 minute, then drain and pat dry. Halve the leeks lengthwise.
In a blender or food processor, combine the vinegar, lemon juice, miso, mustard, mayonnaise, ginger, cayenne and salt and mix for 30 seconds. With the machine on, gradually add the olive oil, then the peanut oil and mix until completely smooth. Scrape the vinaigrette into a bowl.
Spread the cut sides of the leeks with about 2 tablespoons of the miso vinaigrette so it permeates the layers. Cover and refrigerate until ready to serve. To serve, drizzle the leeks with the remaining vinaigrette and garnish with the sliced red pepper. Serve chilled or at room temperature.
The leeks and remaining vinaigrette can be refrigerated separately overnight.