Grease a standard-size loaf pan and line it with a parchment paper sling.
In a small saucepan, combine the butter and milk. Heat over medium-high, just until the butter is melted and bubbles form around the edges of the pan. Whisk in the brown sugar until dissolved. Remove from the heat and cool.
In a large bowl, sift together the oat flour, baking soda, baking powder, ginger, cinnamon, cloves, and salt.
Stir the egg into the cooled butter mixture.
Make a well in the center of the dry ingredients and pour in the butter mixture. Stir until a smooth batter forms.
Heat the oven to 350℉. Pour the batter into the prepared pan and let it rest while the oven heats.
Bake until a toothpick inserted in the center comes out clean, about 45 minutes. Cool in the pan for about 15 minutes, then turn out onto a wire rack to cool completely.
Notes
Flour substitute - If needed, substitute 1:1 all-purpose gluten-free flour for the oat flour or use a single gluten-free flour such as teff flour or brown rice flour.
To make dairy-free: Swap the unsalted butter for non-dairy butter or use vegetable oil for the butter to keep it dairy-free.
Vegan: I haven't tried this recipe with vegan eggs, but I suspect that using 2 flax eggs would be fine if you need to keep this recipe vegan.
Refined sugar-free: Substitute maple syrup, honey, or coconut sugar for the brown sugar.
To serve: I sift a generous amount of powdered sugar over the top of the cake before cutting it into thick slices. To make it fancier, drizzle on some salted caramel sauce or add a spoonful of applesauce or pear sauce alongside. Ice cream is also nice (Screamin' Mimi's peppermint stick or peppermint bark go with this loaf cake perfectly!).