Place the berries into a blender or food processor and blend them to a smooth puree.
Transfer the strawberry puree to a small saucepan and set it over medium heat.
Bring the mixture to a low boil. Lower the heat if needed, so that it's just at a low simmer. Let the mixture simmer, stirring occasionally, until reduced by about half, about 20 minutes. Let the mixture cool while you begin preparing the other ingredients. (Note 3)
Preheat the oven to 350°.
Oil and flour two 9-inch round cake pans, then line the bottoms with parchment paper.
Whisk the flour, sugar, baking powder, baking soda, and salt together in a large mixing bowl.
Transfer the reduced strawberry puree to a liquid measuring cup. You should have about ½ cup. (Note 4)
Add the non-dairy milk to the liquid measuring cup just until you have 1 ¾ cup total liquid volume (made up of the strawberry puree and milk combined).
Stir in the oil, vanilla, strawberry extract, and food coloring, if using.
Add the liquid mixture to the bowl with the dry ingredients. Beat the ingredients together with an electric mixer at high speed just until the batter is smooth, about 1 minute.
Divide the batter among the two baking pans.
Bake the cake layers for 24 to 26 minutes, until a toothpick inserted into the center comes out clean.
Place the cake pans on cooling racks and allow the layers to cool completely before removing them from the pans.