Preheat the oven to 180°C/350°F. Line an 8 x 8-inch pan with parchment paper (lightly grease sides if desired).
In a large bowl, whisk together the dry ingredients: rolled oats, quick oats, sugar, baking powder, cinnamon, and allspice.
In a separate bowl, whisk the wet ingredients until smooth: eggs, milk, vanilla, and almond butter (microwave almond butter 10–15 seconds if very thick).
Pour the wet mixture into the dry and fold until fully combined. If the mixture looks crumbly, add 1–3 tablespoons milk until a thick, scoopable batter forms. Let rest 5 minutes to hydrate.
Scrape the batter into the prepared pan and smooth the top.
Optional cinnamon-sugar swirl/top: Mix 2 tablespoons sugar with 1/2 teaspoon cinnamon. Sprinkle over the surface; for a swirl, drag a knife or skewer in gentle figure-8s.
Bake for 35–40 minutes, until the top is golden, edges are set, and a knife inserted in the center comes out mostly clean.
Cool on a rack for 5 minutes.