Rye Dinner Rolls with Crisp Tops

Stir together yeast, 1/4 cup warm water, and sugar in a large bowl and let stand until foamy, about 5 minutes. (If mixture doesn't foam, start over with new yeast.)
Stir flours, salt, and remaining scant 3/4 cup water into yeast mixture with a wooden spoon until a soft dough forms.
Turn out dough onto a well-floured surface and knead with lightly floured hands until dough is elastic and smooth but still supple and slightly sticky, 6 to 8 minutes. Form dough into a ball.
Put dough in an oiled large bowl and turn to coat. Cover bowl with plastic wrap or a kitchen towel (not terry cloth) and let rise in a draft- free place at warm room temperature until doubled, 1 to 2 hours.
Punch down dough (do not knead). Remove from bowl and fold into thirds like a letter. Divide into 16 pieces and roll each piece into a ball, transferring to a parchment-paper-lined baking sheet and loosely covering with plastic wrap (or towel). Let rise in a warm place until doubled, about 1 hour.
Lightly brush each ball of dough with some of egg white. Gently lay a round of rye-crisp dough, egg-wash side up, on top of each roll. Bake rolls until golden-brown, about 20 minutes. Cool to warm or room temperature.
Stir together flours and salt, then stir in water and oil until a dough forms. Turn out dough onto a lightly floured surface and knead 4 or 5 times. Divide into 16 very small pieces. Roll out each piece on lightly floured surface to a thin round (about 2 inches; shape need not be perfectly round) and arrange in 1 layer on a sheet of parchment.
Beat egg white with a pinch of salt and lightly brush some of it onto rounds. Let stand, uncovered, to dry slightly while rolls rise.
Preheat oven to 425°F with rack in middle.
Lightly brush each ball of dough with some of egg white. Gently lay a round of rye-crisp dough, egg-wash side up, on top of each roll. Bake rolls until golden-brown, about 20 minutes. Cool to warm or room temperature.