Make the ice cream: Pour the heavy cream into a medium bowl and keep cold in refrigerator.
In a small pot over medium heat, warm the milk, sugar, and salt, and cook, stirring occasionally, until sugar is melted, about 3 minutes.
Take 1⁄2 cup of the warm milk mixture and pour over the saffron in the mortar. Let steep for 3 minutes, then pour it back into the warm milk.
Whisk the yolks in a medium bowl.
Pour 1⁄2 cup of the saffron milk into the yolks, whisking constantly, then pour entire mixture back into the hot milk pot to start creating a custard.
Cook the custard slowly, while stirring constantly, preferably with a wooden spoon, about 10–15 minutes. The custard is ready when it gets a little thicker and it coats the spoon.
Use a fine strainer to quickly strain the custard into the cold bowl of cream. Using the back of a spoon, press the saffron as much as possible into the cream.
Let the custard cool down completely. Leave the strainer in the cream to keep extracting the saffron color and flavor. When custard is cool, press saffron again to extract the last of the color and flavor, remove strainer, and churn custard in an ice cream machine 25–30 minutes. Freeze until ready to serve.
Make the filling: Combine all filling ingredients in a large pot. Bring the mixture to a simmer over medium heat and cook until the pears are soft when you put a knife in them, about 10–15 minutes.
Let the pears cool down in the liquid. Once no longer hot, transfer to the refrigerator and continue to cool, ideally overnight. For the galette, cut the pears lengthwise into 1⁄4-inch slices.
Make the dough: Combine sugar, salt, and flour in a mixer at medium speed. Add the cold butter and keep mixing until the butter cubes become the size of peas. Slowly add the water until the dough comes together, but some small, pea-size chunks of butter remain.
Scrape the dough from the bowl and gently form it into a round ball, taking care to not knead it. Wrap tightly in plastic wrap and chill for at least 1 hour.
Make the galette: Preheat the oven to 400°F.
Dust your counter with a little bit of flour. Using a rolling pan, roll the dough into a long rectangle of pastry, about 1⁄4-inch thick. Place the flat dough on a sheet pan lined with parchment paper.
Sprinkle the dough with a little bit of flour. Arrange the sliced pears on the dough, leaving about 1⁄2-inch from the edge clear. Fold the edges of the dough to create a nice edge around the galette.
Brush the folded edge with melted butter and sprinkle with sugar.
Bake for about 35 minutes until golden brown on the edges. Remove the parchment paper and transfer the galette to a cooling rack, discarding parchment paper.
Serve warm with Saffron Ice Cream.