Trim and discard dark green tops and root ends from leek. Split white stalk lengthwise and rinse well to remove dirt between layers. Finely chop leek.
In a 10- to 12-inch frying pan over medium-high heat, stir leek, shallots, garlic, and soybeans in 2 tablespoons olive oil until leek is limp, 6 to 8 minutes.
Place soybean mixture in a food processor and whirl until coarsely puréed. Add remaining 3 tablespoons olive oil, 1 tablespoon at a time, whirling until mixture has a spreadable consistency. Season to taste with salt and pepper. Stir in the chopped mint.
Slice baguette on a slight diagonal into pieces about 1/4 inch thick; reserve ends for another use. Arrange slices on racks on two baking sheets (each 12 by 15 in.). Spray baguette slices lightly with cooking oil spray or brush tops lightly with olive oil. Bake in a 425° regular or convection oven until lightly browned, 6 to 9 minutes.
Spread about 1 tablespoon warm or cool soybean mixture on each slice of toast. Rinse cucumber and thinly slice crosswise. Garnish each toast with a cucumber slice, a fresh mint leaf, and a sprinkling of chili powder. Serve with lime or lemon wedges to squeeze over each just before eating.