Cook the bacon in a large skillet over medium heat until golden brown and crispy, 4 to 5 minutes per side. Transfer to a paper-towel-lined plate to drain. Cut crosswise into thin sticks. Meanwhile, add the beans, sun-dried tomatoes and their oil, 3 tablespoons water, olive oil, vinegar, garlic and 3/4 teaspoon salt to a food processor, and pulse until blended and semi-smooth.
Put 1 slice of bread between 2 pieces of plastic, and roll it flat with a rolling pin. Spread the bread with a heaping tablespoon of the bean puree. Arrange 1 tablespoon of the bacon pieces in a neat row near one edge of the bread. Arrange a neat row of 1 tablespoon grated carrot next to the bacon. Top with 3 to 4 cucumber sticks. Roll up tightly, starting with the bacon end and keeping the ends open. Wrap up tightly with plastic wrap, and refrigerate for at least 30 minutes (this helps the roll-ups keep their shape). Repeat with the remaining ingredients. Keep refrigerated or store in an insulated lunch box with a chill pack for up to 4 hours.
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