Papaya and Jicama Aguachile

Name: Papaya and Jicama Aguachile
Ingredients: ½ cup fresh lime juice (from 6 or 7 limes); 1 serrano chile, stemmed, seeded, and chopped; 1 clove garlic, peeled; ⅓ cup fresh mint leaves; 1 teaspoon whole allspice or peppercorns; 1 ½ teaspoons kosher salt; ½ medium English cucumber, cut into rounds (about 1 cup), divided; 1 pound firm-ripe papaya, peeled, seeded, and cut into 1-in. chunks (about 2 1/2 cups); 1 pound jicama, peeled and very thinly sliced (about 3 cups); ½ medium red onion, thinly sliced (about 1 cup); 2 avocados, chopped; Olive oil, corn tostadas, and saltine crackers, for serving