Preheat oven to 350 F. Grease or line 16 standard muffin tin cups. Set aside.
To make the filling, beat the cream cheese, sugar, egg, and salt together until well-combined.
Stir in the mini chocolate chips.
Set aside.
Melt the 1/2 cup semisweet chocolate chips over hot, not boiling, water, stirring until smooth.
Remove from heat and set aside.
In a large bowl, stir sugar, oil, egg, and vanilla together until well-combined.
Stir in melted chocolate chips.
Add flour, baking soda, and salt. Stir in just until combined.
Mix in the warm water just until combined.
Divide half of the cupcake batter between the muffin tin cups.
Drop a rounded tablespoon of filling in each muffin tin cup.
Top with the remaining half batter.
Bake for 20-25 minutes.
Cool in pan for 5 minutes.
Remove to wire cooling rack to finish cooling.
Video
Notes
Cream cheese: I've used full-fat and reduced-fat cream cheese in this recipe. However, I don't recommend fat-free cream cheese.
Mini chocolate chips: I like to use mini chocolate chips in the filling because they don't sink the way that regular-sized chocolate chips can. You can use regular-sized chocolate chips if you prefer.
Water: The water should be about 80F. Cold water is more difficult to mix in, and the water should not be boiling water.