1. Stir the walnuts in a dry skillet over medium heat until toasted, about 5 minutes. Set aside to cool.
2. Mix 3½ cups bread flour with the brown sugar, yeast and salt in the bowl of a stand mixer fitted with a paddle attachment. 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. Add the milk mixture and 1 egg to the flour mixture. Mix on low speed until a wet coarse ball forms, about 1 minute. 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.
3. 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, 1¾ to 2 hours.
4. 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 1½ times original size, about 1½ hours. Brush rolls with egg glaze; sprinkle with raw sugar. Let rise 15 minutes longer.
5. Meanwhile, position a rack in the center of the oven and preheat to 425 degrees F.
6. 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.
*Note: You can wrap these in foil and place in an airtight bag and freeze for up to 2 weeks. Thaw the rolls at room temperature. If desired, you can rewarm the rolls wrapped in foil in a 350 degree F oven for about 10 minutes.