Prepare an ice bath by filling a bowl with cold water and ice. Set aside. Place goat cheese in a large bowl and set a fine mesh basket strainer over the bowl. Set aside.
In a small saucepan warm milk and sugar over medium heat. Bring mixture to just below a simmer, stirring to dissolve the sugar (the liquid should just begin to bubble).
Meanwhile, whisk the large egg yolks in a bowl until slightly thickened. Slowly, while whisking, pour the hot milk mixture into the yolks. Take your time here so you don’t scramble the egg (this process is known as tempering). Once tempered, return the egg-cream mixture to the saucepan.
Put the saucepan over medium heat and cook, stirring constantly with a wooden spoon. You will know the custard is thick enough when you see steam rise from the surface and the custard coats the spoon. Pour the custard through the mesh basket strainer into the bowl with the goat cheese. Stir until goat cheese is melted. Place the bowl in the ice bath and stir until cool.
Refrigerate until thoroughly chilled. Freeze custard in an ice cream maker according to the manufacturer’s instructions.