In a bowl, whisk flour, baking powder, cardamom and salt; set aside.
In a mixer bowl, cream together butter, sugar, vanilla and milk until light and fluffy. Reserve 1 T of beaten egg in a small container, then add remaining eggs to sugar mixture in three increments, and mix until well incorporated. Scrape the sides and bottom of the bowl from time to time. Add flour mixture all at once and mix on low speed until combined. Add ginger and cashews and combine; do not overwork.
Preheat oven to 350 degrees. Line two large cookie sheets with parchment paper. Lightly dust counter with flour, turn the dough onto counter and divide into fourths. Shape each fourth into a log, approx. 1" thick and 2" wide. If the dough is too sticky to handle, dampen your fingers, then shape. Place two logs onto each cookie sheet. Brush logs with reserved egg. Bake until slightly firm and golden, approx. 25 min. Rotate pans halfway through, if needed. Let cool completely, at least 30 min before continuing.
Reduce oven to 275 degrees. On a cutting board with a serrated knife, cut logs at a slight angle into slices, about 1/2" thick.
Dry biscotti with one of the following methods:
• Lay flat on cookie sheet and bake 20 min, then flip and bake 10-15 min more, until dry.
• Stand biscotti up with a small space between them and bake 20-30 min until dry.
• Place a cookie rack on each cookie sheet with biscotti lying flat and bake 20-30 min until dry.
Let cool completely before storing in an airtight container up to 2 weeks.