Prepare the Tostadas:

1. Fill a large cast iron or sauté pan with enough vegetable oil to reach ½-inch (1.3cm) up the pan and heat it through. Test by adding a corner of one of the corn tortillas; it should bubble when added to the hot oil.
2. Working one at a time, add the tortilla to the hot oil and fry until crispy on both sides, about 1 minute per side.
3. Remove to a paper towel-lined plate and repeat with the remaining tortillas.

Crisp the Shallots:

1. Return the oil used to fry the tortillas to medium heat.
2. Add the shallots to the pan and fry, stirring occasionally, until the shallots are golden brown and crispy, about 6 minutes.
3. Remove to a paper towel-lined plate to drain. The crispy shallots can be made up to a day ahead of time.

Poach the Shrimp:

1. Bring a large pot of salted water to a boil over high heat.
2. Once boiling, remove from the heat, add the shrimp, and poach until the shrimp are opaque and just cooked through, about 3 minutes.
3. Drain the shrimp and set aside to cool completely, about 10 minutes.

Prepare the Coconut Sauce:

1. Heat a large skillet over medium heat.
2. Add the butter and let it melt.
3. Add the ginger and chilies, sautéing until fragrant, about 30 seconds.
4. Stir in the coconut milk and remove from heat. Let cool.
5. Stir in the fish sauce and the whites of the green onion.

Combine and Chill:

1. Chop the cooled shrimp and add to the coconut mixture, stirring to combine.
2. Cover and refrigerate until chilled, about 15 to 30 minutes.

Assemble and Serve:

1. Spoon the shrimp mixture over the fried tostadas.
2. Top with the crispy shallots, the remaining green onion greens, and lime zest.
3. Serve immediately and enjoy!