Prepare the pan. Preheat an oven to 350°F (177°C). Line an 8x8 baking dish with parchment paper leaving enough overhang to easily remove later.
Make browned butter. Place 14 Tbsp (180g) unsalted butter in a medium saucepan over medium heat. Allow the butter to melt, then continue cooking for an additional 5-10 minutes, stirring constantly. You should see the butter begin to foam vigorously – keep stirring. Once the butter begins to turn golden brown and smells nutty, it’s done. Transfer the browned butter to a large mixing bowl before the milk solids burn (and be sure to use a spatula to scrape out all the browned bits!).
Add sugar. Add 1¼ cup +1 Tbsp (300g) brown sugar, then whisk until well combined. Set aside to cool for 5 minutes.
Combine dry ingredients. In a separate bowl, whisk together 2 cups (240g) all-purpose flour, 1¼ kosher salt, 1 tsp ground cinnamon, ½ tsp baking powder, and ¼ tsp ground nutmeg.
Add remaining wet ingredients. Add 2 large eggs (100g), whisking after each addition for about 10 strokes, then add 1 Tbsp vanilla extract and stir to combine.
Fold in dry ingredients. Pour the dry ingredients into the wet ingredients all at once, then gently fold until only a few pockets of flour remain. Add 1 cup (90g) shredded carrots and ½ cup (60g) chopped walnuts, then fold until just fully combined.
Bake the blondies. Pour the blondie batter into the prepared pan, then use an offset spatula to smooth the top into a flat even layer. Bake for 26-28 minutes, or until the top is light golden brown. Cool in the pan on a wire rack.
Make the cream cheese glaze. Place 4oz (113g) room temperature cream cheese and 4 Tbsp (47g) of room temperature butter in the bowl of a stand mixer. Beat on medium speed until light, creamy, and smooth. With the machine off, add ⅔ cup (90g) of powdered sugar. Begin mixing on low speed, then gradually increase (otherwise sugar will fly everywhere). Once smooth, add 1 Tbsp milk, 1 tsp vanilla extract, and a pinch of kosher salt. Continue mixing just until the glaze is a smooth consistency. If you want it slightly thinner, you can add another tablespoon of milk.
Add the glaze. Drizzle all over the top of the cooled blondies, covering the entire surface. If you want to sprinkle extra chopped nuts on top, now is the time to do so. Allow to harden for 10 minutes.
Slice, then enjoy! Once the glaze is set, transfer the blondies from the pan and cut into 9 larger or 16 smaller bars.