Preheat oven to 350°F (175°C). Grease and flour a 9x13-inch baking pan or line with parchment paper.
In a medium bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger.
In a large mixing bowl, beat softened butter and brown sugar until light and fluffy. Add honey and beat until well combined.
Mix in eggs one at a time, then stir in vanilla.
Add dry ingredients in three parts, alternating with milk in two parts, beginning and ending with dry ingredients. Mix gently until just combined.
Pour batter into prepared pan and smooth the top.
Bake 30–35 minutes, or until a toothpick inserted in the center comes out clean.
Cool in the pan for 10 minutes, then transfer to a wire rack to cool completely before slicing.