In double boiler set over simmering water, cook condensed milk, stirring occasionally, until thick and golden, about 2 hours. Or, in microwave-safe bowl, microwave on Medium (50%) for 4 minutes, whisking vigorously twice during cooking. Cook on Medium-Low (30%) for 25 minutes, whisking every 2 to 4 minutes, or until thick and golden.

Let cool for 5 minutes; cover surface of mixture directly with plastic wrap and let cool completely. Let stand at room temperature; do not refrigerate.

Meanwhile, in large, heavy-bottomed saucepan, heat milk over medium heat until hot and bubbles start to form around edge. In bowl, whisk egg yolks; whisk in about ½ cup (125 mL) of the hot milk. Whisk egg mixture back into pan and cook over medium heat, stirring, without boiling, until slightly thickened, about 5 minutes. Remove from heat. Strain through sieve into clean bowl. Add vanilla and half of the caramelized condensed milk; whisk until smooth. Cover surface directly with plastic wrap; refrigerate until cold, 2 hours.

Using ice-cream maker, freeze according to manufacturer's instructions. Spoon heaping tablespoonfuls (15 mL) of remaining caramelized condensed milk into ice cream; swirl in with spatula. Scrape into airtight container; freeze until firm, 4 hours. (Make-ahead: Freeze in airtight container for up to 4 weeks.)