To make the candied pecans, preheat the oven to 250°F (120°C). Line a baking sheet with a silicone mat.
In a small dish, mix the sugar, cinnamon and salt.
Whisk the egg white and vanilla extract until nice and frothy, good 3-4 minutes. (Make sure the mixture is frothy, as pictured above.) Add the chopped pecans and mix well. Using a slotted spoon, remove the nuts and toss the pecans with sugar mixture until the nuts are evenly coated. Transfer the coated pecans onto a prepared baking sheet and spread into a single layer.
Bake the pecans, stirring and checking every 15 minutes, until the nuts are evenly browned and crisp, about 45 minutes. Cool completely on a wire rack. If desired, you can chopped the candied pecans into even smaller pieces.
To make the cake, preheat the oven to 375°F (190°C). Line 17x11in (43x28cm) deep baking sheet with a parchment paper and spray cooking spray all over the parchment paper and on the sides.
In a small bowl, combine flour, baking powder, cinnamon, baking soda, salt and nutmeg. Set aside.
In a mixing bowl with a paddle attachment, mix together eggs, Greek yogurt, oil, sugar and brown sugar until well combined. Add flour mixture and mix just until combined. Don’t overmix at this point. Fold in grated carrots.
Pour the batter into the prepared baking sheet and tap a few times to get rid of bubbles. Bake for 15-18 minutes, or until the top is golden brown and inserted toothpick comes out clean.
Make the frosting while the cake is cooling. Beat butter and cream cheese on medium high speed until fluffy for 1 minute. Add powdered sugar, heavy cream and vanilla extract. Beat on low speed for a minute. Then increase the speed to medium high and continue to beat until smooth and fluffy, about 3 minutes. Transfer into a piping bag with plain round tip, if desired. (Alternatively, you can simply use 2 teaspoons to frost the cakes.)
Once the cake is cooled completely, carefully transfer the cake onto a flat surface. Cut out 2-inch circles using a round cookie, or biscuit cutter. You will get about 35-40 circles, depending how close you cut out the circles. Place the cutout cake layers on wire rack. Pipe about heaping tablespoon of frosting on half of the cake circles. Using an offset spatula lightly spread the frosting and sprinkle candies pecans. Then top with remaining plain cake layers. Frost the second layer the same way and finish with more candied pecans. Store in the fridge, covered, for up to 3 days.
Mix the leftover cake scrapes and buttercream frosting in the mixing bowl with paddle attachment, or using a handheld electric mixer, and make some cake pops.