Heat the olive oil in a large pot over high heat. Add the onions, celery, bell pepper, and Poblano pepper. Cook, stirring occasionally, until the onions begin to brown, 10-12 minutes.
Reduce heat to low. Add the garlic, salt, black pepper, cayenne, thyme, oregano, and cumin. Cook, stirring constantly, for 2-3 minutes.
Add the tomato and cook, stirring occasionally, for 5 minutes.
Add the water and bring the mixture to a boil. Add the navy beans. Cook, covered, for 1 hour.
Remove the lid. Cook uncovered, stirring occasionally, until the beans are tender and the broth has a gravy-like consistency, about 1 hour.
Add the lime juice and coconut milk.
Fry the tortillas: Heat the vegetable oil in a large skillet over medium heat. When the oil is frying temperature (350°), fry the tortillas, one at a time, until brown and very crispy., about 1 ½ minutes on each side. Transfer the fried tortillas to a pan lined with paper towels to drain.
In a food processor, add 1 cup of the navy bean soup. Crumble the fried tortillas into the food processor with your hands. Purée the mixture to form a paste. Fold the tortilla paste into the soup and bring the soup back to a boil.
Optional garnishes: fried julienne tortilla strips, thinly sliced green onions, pickled banana pepper rings.