Make the Glaze
Put the sugar and water in a small saucepan. Bring to a boil for one minute.
Stir in the rosemary, cover and let steep for one hour.
Caramelize the Walnuts
Preheat the oven to 325°F. Line the bottom of a sheet pan with parchment paper
Spread the walnuts on the prepared pan in a single layer. Roast the nuts until they are golden brown, about 20 minutes.
Line the bottom of a second sheet pan with parchment paper or a nonstick baking liner. Measure the butter and put it next to the stove.
Put the nuts, sugar and salt in a medium heavy-bottomed pot. Place over medium-high heat and cook, stirring constantly with a wooden spoon, until the sugar liquefies and coats the nuts. When only a few specks of sugar remain unmelted, remove from the heat and add the butter. Stir until the nuts glisten and start to separate from one another.
Scrape the nuts onto the prepared sheet pan and let them cool for 15 minutes.
Bake the Biscotti
Combine the egg and yogurt in a medium bowl and whisk together by hand. Whisk in the butter. Set aside.
Combine the flour, cornmeal, baking powder, salt and rosemary in the bowl of a food processor. Pulse to incorporate.
Lightly chop warm walnuts and add to flour mixture. Briefly pulse to incorporate, making sure to keep walnut pieces intact. Add the egg mixture and pulse until a dough forms.
Turn the dough out onto a work surface. Cut into two pieces and roll into 12-by-2 inch logs.
Line the bottom of a sheet pan with parchment paper. Place the dough logs on the prepared pan and bake on the middle shelf of the preheated oven for 20 minutes.
Remove from oven and brush rosemary sugar glaze on top. Return to the oven and bake for an additional 10 minutes.
Let cool on a wire rack for 15 minutes.
While the loaves are still warm, using a serrated knife, slice into 1/2-inch rounds on the diagonal.
Place sliced the biscotti on a cooling rack. Place the cooling rack on a sheet pan and toast the biscotti in the oven for 15-20 minutes, until golden brown. Let cool completely before serving.
Store in an airtight container at room temperature.