Preheat the oven to 350F.
Line a 12-hole muffin pan with paper cups.
In a bowl, sift together the flour, baking soda, baking powder and salt. Set aside.
In a large mixing bowl, beat the butter and sugar until light and fluffy. You can do this by hand, with a wire whisk, or an electric mixer. Add the eggs, one at a time, beating after each addition. Stir in the vanilla.
Add the flour mixture and milk alternately, mixing after each addition, starting and ending with the flour.
Divide the batter among the 12 holes of the muffin pan. Each hole should be about 3/4 to 4/5 full. Tap the pan gently to make sure that there are no air pockets at the bottom.
Top each hole with a tablespoonful of strawberry jam. Using the tip of a bamboo skewer, lightly swirl the strawberry jam with the cake batter. Swirl at the surface only — avoid dipping the skewer too deeply into the batter as this may cause the jam to sink.
Bake the cupcakes for 20 minutes in a 350F oven. Cool for about five minutes in the pan then transfer to a wire rack to cool some more.
These strawberry-swirled cupcakes can be served warm or at room temperature.