Preheat the oven to 350°F and grease a 9x13-inch baking pan. In a small bowl, stir together the brown sugar and cinnamon.
In a large bowl, whisk together the flour, sugar, baking powder, baking soda, and salt.
In another bowl, whisk the eggs, sour cream, oil, almond milk, and vanilla until smooth. Pour into the dry ingredients and whisk just until the batter is smooth with no dry pockets.
Spread half of the batter into the prepared pan and sprinkle the cinnamon sugar evenly over it. Spoon the remaining batter over the top in dollops and gently spread to cover.Drag a skewer through the batter in a zigzag pattern to create gooey cinnamon swirls.
Bake for 35 to 40 minutes, until golden and a toothpick comes out clean, aside from a little sticky swirl.
While the cake bakes, whisk together the powdered sugar, almond milk, honey, and vanilla until smooth.
Poke the warm cake all over with a skewer and pour the glaze evenly over the top, spreading it to the edges. Let it cool for 20 to 30 minutes so the glaze soaks in and sets slightly, then serve warm.