Heat oven to 350°F. Toast walnuts on a small sheet pan for 6 to 8 minutes until fragrant, then cool for 10 minutes and pulse into fine crumbs without making nut butter.
Chop the dry watercress finely. Beat softened butter with salt and pepper, then fold in the greens and walnut crumbs until evenly distributed.
Spread the mixture evenly over one face of all 12 bread slices, working gently so the soft crumb doesn’t tear. Pair the slices with their filled faces inward to make six sandwiches.
Cover and refrigerate for 10 minutes to firm the butter slightly. Trim crusts with a serrated knife and cut each sandwich diagonally in both directions.
Yield 24 small triangles, two per serving. Keep covered and refrigerated until serving within 24 hours; let the portion being served stand for about 5 minutes so the butter loses its refrigerator hardness.