Preheat oven to 350F and grease two 8x4" loaf pans.
If using canned peaches, drain the juice, reserving it if you plan to use it in the glaze.
In a mixing bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, and nutmeg. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment (or in a large mixing bowl with a handheld electric mixer), mix together vegetable oil and sugar on medium speed.
Reduce speed to low and add eggs, one at a time, mixing well after each addition.
Add vanilla extract and diced peaches, mixing to combine.
With the mixer still on low speed, gradually add the flour mixture to the wet ingredients, mixing just until fully incorporated, scraping down the sides of the bowl as needed.
Divide batter between the prepared pans. Bake for 50-60 minutes, or until a toothpick inserted in the center of the bread comes out clean.
Remove from oven and let bread cool in the pans for about 10 minutes, then invert onto a cooling rack or serving plate to cool completely.
Once the bread is cooled, prepare the glaze, if using. Combine powdered sugar and 2 tablespoons of peach juice or milk in a small bowl. Whisk together until smooth. If the mixture is too thick, add more juice or milk, a teaspoon at a time, until desired consistency is reached. Drizzle over bread, then let it sit for about 10 minutes so the icing can harden.