Heat the vegetable oil in a small wok or saucepan over high heat until shimmering hot. In a small bowl, mix the garlic with the cornstarch and a pinch of salt. Put the garlic mixture in a fine sieve and shake to remove the excess cornstarch. Fry the garlic in the oil, stirring gently, until the garlic is light golden, about 1 minute. Immediately strain the garlic and oil through the sieve set over a bowl. Transfer the garlic to a paper-towel-lined plate, dab gently with paper towels to absorb excess oil, and let cool to room temperature. Reserve the garlic-flavored oil in the refrigerator for another use (such as vinaigrettes or grilled bread).

Heat the oven to 275 degrees F. Pulse the bread in a food processor until the crumbs are uniform in size, 5 or 6 pulses. In a large bowl, mix the crumbs with the olive oil or butter until evenly coated. Transfer the crumbs to a rimmed baking sheet and bake, stirring once or twice, until golden brown, 20 to 30 minutes. Let the crumbs cool to room temperature. Transfer the crumbs to a medium, shallow serving bowl and stir in 1-1/2 teaspoons of the reserved fried garlic. Save the remaining garlic for the mayo.

In a small bowl, mix the mayonnaise, cilantro, scallion, jalapeno, lime juice, 1 teaspoon salt, and the remaining 2 tablespoons fried garlic. Add more jalapeno and salt to taste. Transfer to a small serving bowl.

Bring 7 cups of very well salted water to a boil in a 3-quart saucepan over high heat. Add the shrimp, stir once or twice, and poach until just cooked through, 1-1/2 to 2 minutes (the water will not return to a boil). Drain the shrimp and let them cool for 10 minutes. Transfer the shrimp to a platter and serve them slightly warm or at room temperature with the mayo and breadcrumbs.

The breadcrumbs and mayo may be prepared up to 1 day ahead. Store separately in airtight containers; refrigerate the mayo.