Preheat your oven to 350°F and grease a 9x13 inch baking dish (or similar 13-cup capacity pan). While the oven heats, spread the pecans on a separate baking sheet and toast them for 8 to 12 minutes, stirring halfway through, until fragrant and lightly browned. Remove from the oven and let cool completely on the baking sheet—this prevents them from continuing to cook and becoming bitter. Once cooled, chop them into roughly 1/4-inch pieces and set aside.
In a medium bowl, whisk together the flour, cinnamon, baking soda, salt, nutmeg, baking powder, and ginger. This ensures the leavening agents and spices are evenly distributed throughout the cake. While you're doing this, use a box grater's small holes to grate the carrots, measuring out 2 2/3 cups. I like to grate them just before mixing so they stay fresh and release their moisture at the right time.
In a large mixing bowl, whisk together the sugar and room-temperature eggs until well combined and slightly pale, about 1 to 2 minutes. This helps aerate the batter and creates a lighter crumb. Whisk in the vegetable oil, Greek yogurt, and vanilla until fully incorporated and smooth. The room-temperature eggs are essential—they emulsify much better than cold eggs and create a more cohesive batter.
Add the dry ingredient mixture from Step 2 to the wet ingredients from Step 3 and stir until just combined—don't overmix, as this can develop too much gluten and make the cake tough. Fold in the grated carrots and toasted pecans from Step 1 with a final few gentle folds to distribute them evenly. Pour the batter into your prepared pan and smooth the top gently.
Bake at 350°F for 35 to 40 minutes, until a toothpick inserted in the center comes out with just a few moist crumbs (not wet batter). The cake should be golden brown and spring back lightly when touched. Remove from the oven and let it cool completely in the pan before frosting—this prevents the frosting from melting and sliding off.
While the cake cools, make the frosting by beating the softened cream cheese and butter together in a medium bowl with an electric mixer for about 2 minutes until smooth and creamy. Gradually add the sifted powdered sugar and vanilla, beating on medium speed until light and fluffy, about 3 to 4 minutes. I always sift the powdered sugar before adding it to prevent lumps—this extra step makes the frosting silky smooth and easier to spread.
Once the cooled cake is ready, spread the frosting evenly over the top using an offset spatula or the back of a spoon. Sprinkle the toasted pecans from Step 1 over the frosting, pressing them gently so they stick. Cut into squares and serve at room temperature or refrigerated, depending on your preference.