Trim asparagus to 3 1/2-inch lengths measured from the tips, reserving the lower tender portions for another meal. Steam the tips over boiling water for 3 to 4 minutes until tender but still green.
Transfer asparagus to ice water for 2 minutes, then drain and spread on clean towels. Blot very thoroughly, including between the tips, and let stand for 5 minutes.
Beat cream cheese with Asiago, lemon zest and pepper. Spread one face of all 16 bread slices with a thin even layer.
Arrange six asparagus tips on each of eight slices in three evenly spaced pairs, all pointing in the same direction. Close with the other slices, spread sides inward, and refrigerate covered for 10 minutes.
Trim crusts without cutting through the asparagus tips. Cut each sandwich lengthwise into three fingers between the pairs, leaving two spears inside every finger; yield 24 pieces, two per serving.
Keep the sandwiches covered and refrigerated and serve the same day, lifting them with a small spatula so the fillings stay aligned.