Heat a large skillet over medium heat. Add the ground chicken, onion, ground coriander, ground cumin, and salt. Cook, stirring frequently, until the chicken is no longer pink and the onion is softened. Drain any excess grease if needed.

Stir in the diced tomatoes with their juices, potatoes, chopped dried plums, and quartered olives until evenly combined.

Bring the mixture to a boil. Reduce the heat to low, cover, and simmer for about 10 minutes, or until the potatoes are fork tender.

Remove the lid and continue cooking for 3 to 5 minutes, stirring occasionally, until most of the liquid has evaporated. Remove from the heat and let the mixture cool slightly.

Arrange the tostada pieces on a large serving platter or divide them among individual serving bowls. Top with the shredded lettuce, warm chicken picadillo mixture, Monterey Jack cheese, sliced green onions, and chopped cilantro. Serve immediately.