For the crust, preheat oven to 400°F.

Stir cooled sauce with a whisk and serve sauce on the side with a pear half.

Process graham sticks in a food processor until almost ground to a powder.

Add almonds and sugar and process until almonds are chopped finely.

Transfer crumb mixture to a medium-sized mixing bowl and pour in butter. Stir until crumbs are thoroughly moistened.

Press crumb mixture into the bottom of a 9-inch springform pan.

Place pan on a baking sheet and bake until crust is golden brown and firm, about 10 minutes.

For the cheesecake, reduce oven heat to 325°F.

Place cream cheese, goat cheese, lemon zest, lemon juice and vanilla in a large mixing bowl.

With an electric hand mixer, beat until just smooth, scraping down sides of the bowl as needed.

In two or three additions, beat in sugar until mixture is creamy.

Add eggs, one at a time, beating and scraping down sides of the bowl after each addition. Continue to beat until mixture is very smooth.

Pour batter into prepared crust.

Bake until edges of cheesecake look set and the center is still soft and slightly jiggly, 50 to 60 minutes.

Place pan on a rack to cool completely in the pan.

Then cover and refrigerate for at least 6 hours or overnight.

Increase oven temperature to 400°F.

For the roasted pears, halve them and scoop out cores with a spoon or melon baller.

Put butter, lemon juice, a tablespoon of maple syrup and 1/4 cup of pear juice in a medium baking dish.

Bake for a minute or two, just until butter melts.

Swirl to mix ingredients, then place pears, cut side down, in dish along with rosemary sprigs.

Bake for 15 minutes, then turn pears and baste with cooking liquid.

Continue to bake another 5 minutes until pears are tender.

Transfer pears to a plate to cool.

Place remaining 3/4 cup pear juice and 3 tbsp maple syrup in a small saucepan.

Strain juices from baking dish into saucepan.

Bring mixture to a boil.

Stir in cornstarch-water mixture and cook, stirring, until mixture thickens slightly, about a minute.

Transfer pear sauce to a small bowl to cool.

When cheesecake has thoroughly chilled, unmold from pan.

Carefully cut into slices with a warm knife (dip knife in hot water and wipe dry).