Preheat your oven to 350°F (175°C) and grease a loaf pan to prevent sticking.
In a large mixing bowl, whisk together the eggs, pumpkin puree, and vegetable oil until the mixture is smooth and well combined, and the eggs are slightly doubled in volume.
Add the vanilla extract and brown sugar to the wet ingredients and stir until the sugar begins to dissolve, creating a slightly thickened batter.
In a separate bowl, sift together the flour, cinnamon, nutmeg, and salt to evenly distribute the spices and prevent clumping.
Gradually fold the dry ingredients into the wet mixture using a spatula, mixing gently just until combined—being careful not to overmix to keep the bread tender.
Fold in the chopped walnuts, ensuring they are evenly distributed throughout the batter.
Pour the batter into your prepared loaf pan, smoothing the top with a spatula to ensure even baking.
Bake in the preheated oven for about 50-55 minutes, or until a toothpick inserted in the center comes out clean and the top is golden brown.
Remove the loaf from the oven and let it cool in the pan for 10 minutes, then transfer it to a wire rack to cool completely for best slicing.
Once cooled, slice the bread and enjoy its moist, aromatic crumb with the crunchy walnuts adding texture with every bite.