Warm the 1 tablespoon olive oil in a small sauté pan, add the prosciutto, and cook, stirring often, over low heat until crispy. Remove the prosciutto bits with a slotted spoon and spread them on a paper towel–lined plate.

Bring a medium pot of water with 1 tablespoon salt to a rolling boil. Add the baking soda, then add 6 of the eggs. Boil for 4 minutes, 45 seconds, then transfer the eggs to an ice-water bath. Chill completely, about 10 minutes. Gently peel the eggs and reserve.

In a large sauté pan, bring the 3/4 cup olive oil, 3/4 cup water, and 1 teaspoon salt to a boil, then lower the heat so the poaching liquid simmers. Working in batches, add the asparagus in a single layer so it’s barely submerged in the liquid. Poach at a simmer until the asparagus is just tender, 3 to 5 minutes. Transfer to a baking sheet in a single layer.

Put the flour in a small bowl. In another small bowl, beat the remaining 2 eggs. Put the breadcrumbs in a third small bowl. One at a time, gently roll the reserved soft-boiled eggs in the flour to coat, then dip in the egg, letting the excess drip off, and then in the breadcrumbs.

In a small pot, pour 3 inches of canola oil and heat to 375°F on a candy thermometer. Carefully adding 2 of the breadcrumb-coated eggs at a time, fry until golden brown, about 1 minute. Transfer to a paper towel–lined plate.

To serve, arrange the asparagus on a platter. Top with the crispy eggs. Spoon the crema around the spears, then garnish with a generous sprinkling of salt and prosciutto bits.