Preheat oven to 350°F/175°C. If using a 9x13 baking pan, grease and flour the bottom and sides of the pan. If using two 9-inch cake pans, grease bottoms and sides of the pan and cut rounds out of parchment paper to place in the bottom of the pans. Then grease the parchment too.
Prepare Strawberry Reduction: Wash strawberries and cut off the stems. Place them in a food processor and pulse in short bursts until the strawberries are broken down in a thick slurry, with some strawberry chunks. Pour this into a saucepan over medium heat until it simmers. Turn heat down to low and cook for 30 to 40 minutes, until this mixture reduces to approximately ½ cup. Transfer to a bowl and refrigerate while you prepare the rest of the cake.
Whisk together the flour, sugar, baking soda, and salt in a large bowl.
In a separate bowl combine the water, vegetable oil, extract, apple cider vinegar, cooled strawberry mixture, and natural food coloring (if using). Stir to combine. You might need to mash the strawberry reduction to get it to separate a bit.
Add the strawberry mixture to the dry ingredients and stir until there are no visible clumps of flour in the batter.
Pour the cake batter into the prepared pan(s). For the 9x13 pan, bake for 45 to 50 minutes. For the two round cake pans, bake for 30 to 35 minutes. A tester inserted in the middle of the cake should come out mostly clean and the edges of the cake should pull away slightly from the pan.