How to Make It
Preheat the broiler. Arrange the tomato halves, cut sides down, on a baking sheet and drizzle with the 1 tablespoon olive oil. Broil for about 3 minutes, or until the skins are charred. Transfer the broiled tomatoes to a large nonreactive saucepan, add the Vegetable stock and bring to a boil over high heat. Reduce the heat to low and simmer for 20 minutes. Strain the stock.
Meanwhile, roast the poblano and Anaheim chiles directly over a gas flame or under the broiler until charred all over. Transfer the chiles to a paper bag and let steam for 5 minutes. Peel the chiles and discard the stems, ribs and seeds. Cut the chiles and discard the stems, ribs and seeds. Cut the chiles into 2-by-1/4-inch strips.
Heat the remaining 1/4 cup olive oil in the large nonreactive saucepan. Add the onions, jalapeños and garlic and cook over moderately high heat, stirring occasionally, until the onions are softened, about 5 minutes. Add the beer and boi for 3 minutes. Add the strained stock, roasted chiles, potatoes, lime juice, achiote paste and sugar. Lower the heat to moderate and simmer until the potatoes are tender, about 20 minutes. Season with salt and pepper. Stir in the chopped cilantro. Ladle the soup into shallow bowls and garnish with the cheese and cilantro leaves.