Preheat the oven to 350°. Line a standard muffin with 12 cupcake liners. Set aside.
Add lemon juice and zest, 1 cup of diced strawberries, and 1 teaspoon of sugar to a blender. Blend at high speed for 1 minute or until the strawberries are completely pureed. Set aside.
Whisk together the flour, baking powder, and salt in a small bowl.
In a separate large bowl, combine the vegetable oil and 1/2 cup of sugar and whisk until mixed.
Add the eggs, one at a time, along with the yogurt, and whisk until smooth.
Pour in 1/2 cup of strawberry puree and stir. Add in 1/2 of the dry ingredients and stir until well-mixed. Add the remaining dry ingredients and continue stirring until just blended. A few small lumps are fine.
Spoon 1/4 cup of batter into each cupcake liner, about 2/3 full.
Bake for 15-20 minutes, or until a toothpick poked into the center cupcakes comes out clean. Rest on a cooling rack for about 20 minutes.
Frosting
In a large mixing bowl, cream the butter with an electric hand mixer at medium speed until smooth.
Gradually add the powdered sugar, a pinch of salt, and continue mixing at medium speed. Add the strawberry preserves, and beat until well mixed.
If the buttercream is too thick and stiff, add the milk, 1 tablespoon at a time, until smoother.
Spoon the buttercream into a piping bag with a large star tip. Pipe the buttercream onto the cooled cupcakes, and top with halved strawberries.
Serve at room temperature or chilled.
Notes
You can use the extra strawberry puree in the buttercream instead of the strawberry preserves. However, we found that this can result in a thinner, less stable buttercream because of the extra liquid in the puree.