Preheat broiler and lightly oil a shallow flameproof baking pan with olive oil.

Cut each block of tofu crosswise into 6 slices and pat dry between several layers of paper towels. Arrange in 1 layer in baking pan and brush tops of slices with more olive oil. Broil 4 to 6 inches from heat, without turning, until golden brown, about 15 minutes.

While tofu is broiling, purée cilantro, pine nuts, lime juice, fish sauce, sesame oil, sugar, remaining ¼ cup olive oil, salt, and pepper in a food processor until bright green and smooth, about 1 minute.

Transfer tofu with a slotted spatula to a platter and serve with cilantro pesto.