In the bowl of a food processor, finely chop the peeled garlic cloves. With a very sharp knife, slice the ramps across the grain of the bulb—this technique will protect the delicate herbs from discoloring and oxidizing as quickly. Hold the whites and the green separately.
In a small saucepan set over medium-low heat, warm the olive oil. Add the chopped garlic and chopped whites of the ramps and cook over medium-low until the garlic is soft and slightly toasted, about 10 to 12 minutes. Add the chopped ramp greens, 2 tablespoons of the lime juice, salt (usually ¾ teaspoon) and green chile and let cook for another 2 to 3 minutes. Remove from the heat and let cool to room temperature.
If the shrimp is on the bigger side, coarsely chop it into ¼” pieces.
In a large mixing bowl, dress the cooked shrimp with the remaining lime juice and a healthy portion of the green mojo. If there’s any left, it will keep in the refrigerator for at least a month. Gently fold in the avocado and cucumber. Check the mixture for seasoning, and add a little more salt if necessary.
Spoon generous spoonfuls of the shrimp on the tostadas, garnish with the fresh herbs and serve to your guests.