Preheat oven to 350F degrees.
Prepare the cake pans: Trace a circle of parchment paper around the bottom of each pan. Cut out the circles and place them on the bottoms of the cake pans. Then, coat the bottoms and sides of the cake pans with nonstick cooking spray.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugar until fluffy. Beat in the eggs, milk and strawberry extract. Finally, beat in the strawberry sauce. (Alternatively, this can be done in a large mixing bowl using a handheld electric mixer.)
In a separate bowl, whisk together the flour, salt and baking powder.
With the mixer running on low speed, add the flour mixture to the wet ingredients until incorporated. Add the drops of food coloring now, if you are using them.
Divide the batter as evenly as possible among the cake pans. Bake for 25 minutes. Cool the cake pans completely on wire racks before removing the cakes.
While the cake is baking, remove the stems from the fresh strawberries and place them into the bowl of a food processor or high speed blender. Puree the strawberries until smooth. Set aside.
Make the frosting: In the bowl of a stand mixer fitted with the paddle attachment, beat the butter until fluffy. Slowly add the powdered sugar in small increments. Then, beat in the strawberry puree and heavy cream.
Assemble the cake: Place the first layer of cake on a serving plate or cake stand. Spread half of the strawberry jam evenly across the surface. Place the second layer of cake over it. Spread the remaining jam. Top with the third cake layer. Using a spatula or dull knife, spread the frosting onto the top of the cake and around the sides. Garnish with additional fresh strawberries, if desired.