Caramelized Pear Frozen Yogurt

I have always been obsessed with pear ice cream or pear gelato and they are hard to find in the USA.
This recipe is absolutely delicious!!!
First, prepare the caramelized pears...
Dice 3 fresh pears. Melt 3/4 cup of sugar in a thick saucepan on medium heat till the sugar starts to brown slightly at the edge, add a pinch of salt (like Fleur de Sel or sea salt, do not stir), add the diced pears, the caramel will bubble and parts will become sticky, not to worry, stir and continue to cook on medium heat till all the caramel is melted and pears are golden brown (watch the caramel carefully as it can easily burn). Remove from heat and let cool. Put in blender and puree. Put in freezer till very cold.
Prepare the frozen yogurt:
- 1-2/3 cup whole milk
- 3/4 cup granulated sugar
- 4 cups of Greek plain yogurt
- 1/4 cup heavy cream
- 1 tablespoon of rum
Mix the milk with sugar till dissolved, add the yogurt, cream, rum, stir well. Turn the ice-cream maker on, pour the mixture into the freezer bowl and  mix till thickened, about 20 mn. Add the caramelized pear puree. Continue to mix in machine for another 5 mn. It's delicious eaten right away (with a soft texture), or put in the freezer for couple of hours for a firmer consistency...