In a large mixing bowl, whisk together 2 1/4 cups flour, 2 tsp baking powder, 1/2 tsp baking soda, and 1 tsp salt. Set aside.
In a stand mixer or large bowl using a hand mixer, cream 1/2 cup softened butter with ¾ cup granulated sugar until light and fluffy, about 2–3 minutes. Add the 2 eggs, one at a time, mixing well after each addition. Then mix in 1 tsp vanilla extract.
Add half of the dry ingredient mixture to the bowl and mix on low. Pour in half of the 3/4 cup eggnog and continue mixing. Add the remaining dry ingredients and the rest of the eggnog, mixing just until combined. Avoid overmixing—a few light streaks of flour are okay.
Gently fold in 1 1/2 cups fresh cranberries with a spatula until evenly distributed throughout the batter.
Line a 9x5-inch loaf pan with parchment paper and spread the batter evenly into the pan. Bake at 350°F (175°C) for 60–75 minutes, tenting with foil halfway through to prevent over-browning. The loaf is done when a toothpick inserted into the center comes out with moist crumbs rather than wet batter.
Allow the loaf to cool in the pan for 10–15 minutes, then transfer to a wire rack to cool completely.In a small bowl, whisk together 4 tbsp powdered sugar and 1 tbsp eggnog to create the glaze. Drizzle over the cooled loaf before slicing.