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Cook bacon in a 12-inch heavy skillet over moderate heat, turning occasionally, until crisp, then transfer with tongs to paper towels to drain.
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Stir together mayonnaise, chives, dill, and salt and pepper to taste in a small bowl.
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Halve, pit, and peel avocado, then slice lengthwise. Gently toss slices with lemon juice.
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Make sandwiches with toast, herb mayonnaise, avocado, bacon, and sprouts, seasoning with salt and pepper.