Preheat the oven to 275 degrees . Butter and flour an 8-inch square baking pan. In a medium saucepan, melt the chocolate chips with the milk and heavy cream over low heat. Add the butter and sugar and stir until smooth. Remove from the heat.
In a medium bowl, sift together the flour, baking soda and salt. Add to the chocolate mixture and stir until smooth. Whisk in the egg and vanilla. Pour the batter into the prepared pan and bake until a toothpick inserted in the center comes out clean, about 30 minutes.