Preheat your oven to 350°F (175°C). Prepare a 10-cup bundt pan by greasing and flouring it thoroughly.
In a medium-sized bowl, whisk together the flour, baking soda, cinnamon, and salt. Set aside.
In another bowl, combine 1 cup of sour cream with the vanilla extract and set it aside for later use.
Using a mixer, beat the softened butter on medium speed until it's smooth and creamy. Gradually add both the granulated sugar and the light brown sugar, mixing on medium speed for about 3-5 minutes until the mixture becomes light and fluffy.
Crack the eggs one at a time into the batter, ensuring each yolk is well blended before adding the next.
With the mixer set to low speed, begin adding the dry flour mixture alternately with the sour cream mixture. Start and finish with the dry ingredients, adding the flour in three parts and the sour cream in two parts. Be careful to mix just until combined—over-mixing may result in a dense cake.
Gently fold the diced peaches and crushed pecans into the cake batter, making sure they are evenly distributed.
Pour the batter into your prepared bundt pan, smoothing the top for even baking.
Bake in the preheated oven for approximately 1 hour, but start checking at around 50 minutes. The cake is done when a toothpick inserted in the center comes out clean or with only a few moist crumbs attached. Baking times may vary depending on the type of pan used, so keep an eye on it toward the end.
Allow the cake to cool for 10 minutes in the pan before carefully inverting it onto a cooling rack. Be cautious not to let it sit too long, or it may stick to the pan.