Quarter the leek lengthwise, and slice crosswise into 1/4-inch-thick pieces. Place in a large bowl of cold water, and leave for 5 to 10 minutes to rid the pieces of dirt and sand. Using a slotted spoon, lift leek pieces out of water, and drain.
In a medium skillet, heat 1 tablespoon olive oil over low heat; add garlic, shallots, leek, and salt and pepper. Cook until very soft but not browned, about 15 minutes. Add peas, raising the heat to medium, and cook, stirring, until peas are heated through, 3 to 5 minutes.
Transfer the pea mixture to a food processor. Add chicken stock and the remaining tablespoon olive oil; pulse until mixture is a coarse puree, about 12 pulses. Transfer half the puree to a medium bowl. Process the remaining half of the peas for 15 seconds, then combine with the coarsely pureed peas. Stir in chopped mint. Adjust seasoning with salt and pepper, if necessary.
Cut bread into 1/4-inch-thick slices, brush with oil, and toast under the broiler on both sides until golden brown. Spread the pea mixture on the toasted bread, and serve immediately or at room temperature.