In a small ovenproof pan set over high heat, sauté the shallots in 1 tablespoon of the olive oil until they begin to sizzle. Sprinkle with salt. Cover with lid or foil and bake in the oven for 10-15 minutes, until just tender. Remove from the oven and cool.
In a large saucepan, bring water to a simmer. Add white vinegar. One by one, crack the eggs into the water, and poach until the whites are cooked. Remove from the water and place in a bowl of ice water to cool.
In a medium pan over high heat, add the remaining olive oil and heat until shimmering. Add the asparagus and cook for 3-5 minutes, until lightly browned. Add roasted shallots to the asparagus and cook together for 30 seconds. Take the pan off the heat and add the mustard seeds. Toast for 30 seconds. Add stock to prevent further browning. Stir in lemon juice, mustard, and red wine vinegar.
On a large plate, dress the salad with warm mustard vinaigrette, and top with asparagus, shallots, slices of prosciutto, and poached eggs.