Set the oven to 350°F. Spray a 9x5 loaf pan with nonstick cooking spray, then fit a piece of parchment paper in the bottom of the pan. Place aside.
Walnuts should be stirred and heated gently, being careful not to burn them, in a small pan. Remove from heat and leave to cool.
Beat the egg and egg white until foamy in a large bowl. Beat again after adding the sugar, buttermilk, and vanilla.
Combine the flour, baking soda, salt, cinnamon, and nutmeg in a separate basin. Mix well before adding the flour mixture to the wet mixture.
Add the oil and give it a quick toss before folding in the cut strawberries and toasted walnuts. Stir just enough to mix. Pour into the loaf pan, then evenly level the top down. When a toothpick put in the center of the cake comes out clean, bake for 40 to 45 minutes. After the loaf has cooled in the pan for 15 minutes, remove it and enjoy.