Preheat the grill or broiler.
Run the meat through the second-smallest setting on a meat grinder. If you do not have a meat grinder, chop the meat very fine with a very sharp knife.
In a small bowl, combine the mustard, olive oil, diced onions, capers, and lemon juice and stir well.
In a large bowl, combine the ground lamb, mustard mixture and the jalapeno pesto, and mix well with your perfectly clean hands.
Grill or broil the bread slices for 2 minutes on one side.
Divide the meat mixture into four portions and mound in the center of four chilled dinner plates. Spread the baguette slices with the mint-onion jam and arrange around the tartare. Make a small indentation with your thumb in the center of each mound of meat. Crack one egg into each indentation, drizzle the plates with the Da Vero oil, and serve immediately.
For the Mint and Onion Jam:
In a 12- to 14-inch sauté pan, heat 1 tablespoon of oil over medium heat. Add the onion rings, season with salt, pepper, and 1 tablespoon of the sugar, and cook over medium-low heat until the onions are soft and translucent, about 10 minutes; do not brown. Cool to room temperature.
In a blender or food processor, combine the cooked onions, the remaining tablespoon of sugar, 1 teaspoon of salt, the red pepper flakes, and the remaining 1½ cups of olive oil. Blend until the mixture is a coarse puree. Add the mint leaves in batches, pureeing after each addition. When all of the mint leaves have been incorporated, add the chopped onion and puree again. The jam can be kept, in an airtight container in the refrigerator, for up to 1 week.
For the Jalapeño Jam:
Combine the peppers, almonds, and onion in the bowl of a food processor. Pulse until pureed, then slowly drizzle in the oil until emulsified. Jalapeno pesto can be stored for up to 1 week, refrigerated, in an airtight container.