Pour the skim milk into a large saucepan and place over medium heat. Heat to 120 degrees F. Remove from the heat and gently pour in the vinegar. Stir slowly for 1 to 2 minutes. The curd will separate from the whey. Cover and allow to sit at room temperature for 30 minutes.
Pour the mixture into a colander lined with a tea towel and allow to sit and drain for 5 minutes. Gather up the edges of the cloth and rinse under cold water for 3 to 5 minutes or until the curd is completely cooled, squeezing and moving the mixture the whole time. Once cooled, squeeze as dry as possible and transfer to a mixing bowl. Add the salt and stir to combine, breaking up the curd into bite-size pieces as you go. If ready to serve immediately, stir in the half-and-half or heavy cream. If not, transfer to a sealable container and place in the refrigerator. Add the half and half or heavy cream just prior to serving.