Line a sheet pan with parchment paper. Melt the chocolate in a heatproof bowl set over a pan of boiling water, being careful not to let the water touch the bottom of the bowl, and stir constantly until just melted. Remove from the heat and pour 5 oz [142 g] of the chocolate onto the prepared pan and freeze until firm, 10 to 15 minutes.
In a large bowl, whisk together the sweetened condensed milk, vanilla, salt, and remaining 3 oz [85 g] of melted chocolate until completely combined.
In the bowl of a stand mixer fitted with a whisk, beat the cream cheese on medium speed until smooth. Turn the mixer to low speed and add the heavy cream in a slow, steady stream, mixing until combined. Increase the speed to medium-high and whisk until stiff peaks from, 3 to 4 minutes.
Add half of the whipped cream to the sweetened condensed milk mixture and whisk until completely combined. Using a rubber spatula, gently fold in the remaining whipped cream mixture until no streaks remain.
Remove the chocolate from the freezer and chop it into bite-sized pieces. The chocolate will begin to melt as you touch it, so work quickly. Add the chopped chocolate to the ice cream and mix to combine. Pour into a 9 by 4 by 4 in [23 by 10 by 10 cm] Pullman loaf pan with a lid and freeze until firm, 6 hours, or up to 1 week.