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1
Stir the walnuts in a dry skillet over medium heat until toasted, about 5 minutes. Set aside to cool.
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2
Mix 31/2 cups bread flour with the brown sugar, yeast and salt in the bowl of a stand mixer fitted with a paddle attachment.
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3
Warm the milk in a small saucepan over low heat until an instant-read thermometer inserted into the milk registers 95 degrees F. Add the oil; remove from the heat.
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4
Add the milk mixture and 1 egg to the flour mixture. Mix on low speed until a wet coarse ball forms, about 1 minute.
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5
Add the nuts and the cranberries. Replace the paddle attachment on the mixer with a dough hook. Mix dough on low speed until smooth, elastic, and slightly tacky, adding more flour by the tablespoonfuls as needed, about 4 minutes. Transfer the dough to a floured surface and knead for about 2 minutes.
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6
Lightly oil a large bowl. Shape the dough into a ball; place in the prepared bowl, turning to coat with oil. Cover with plastic wrap and let the dough rise at room temperature until almost doubled in volume, 13/4 to 2 hours.
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7
Line a large baking sheet with parchment paper. Transfer the dough to an unfloured surfaced; divide into 12 equal pieces. Shape each piece of dough into a smooth round ball. Transfer the rolls to the prepared baking sheet, spacing them apart. Spray the rolls with nonstick spray. Cover loosely with plastic wrap; let rise at room temperature until 11/2 times original size, about 11/2 hours. Brush rolls with egg glaze; sprinkle with raw sugar. Let rise 15 minutes longer.
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8
Position a rack in the center of the oven and preheat to 425F,.
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9
Place rolls in oven; reduce oven temperature to 400 degrees F and bake 7 minutes. Rotate baking sheet; continue to bake rolls until golden and slightly firm to the touch, about 8 minutes longer. Cool completely on a cooling rack.
