Preheat oven to 300°F (150°C).Place almonds and pistachios on a small baking sheet. Bake for 12 minutes. Turn oven off, and leave nuts in oven to keep warm.Line an 8-inch square metal baking pan with parchment paper, letting excess extend over sides of pan.In a small saucepan, bring honey to a boil over medium heat. Boil until mixture registers 252°F (122°C) on a candy thermometer.In another small saucepan, heat sugar, corn syrup, and ½ cup (120 grams) water over medium heat. Cook until mixture registers 295°F (146°C) on a candy thermometer. Remove from heat; stir in amaretto and almond extract.In the bowl of a stand mixer fitted with the whisk attachment, beat egg whites at medium speed until foamy. Add cream of tartar, and beat until stiff peaks form. Add hot honey in a slow, steady stream until combined, about 3 minutes. Switch to the paddle attachment. With mixer on medium-high speed, add hot sugar mixture in a slow, steady stream, and beat for 15 to 25 minutes, depending on humidity. The longer the nougat is mixed, the harder the end product will be. If you want a softer nougat, mix for only 10 to 15 minutes. Nougat is ready when you can pinch off a small amount and roll it between your fingers without it sticking once cooled. (Be careful, your nougat will still be quite hot.)Add warm nuts, and stir well with a greased spatula. (Nougat should be very thick and very hard to stir.) Sprinkle half of cherries in prepared pan. Using a greased plastic bench scraper, add half of nougat. Press down with greased hands. Sprinkle with remaining cherries. Add remaining nougat, and smooth top with a greased spatula. Cover with parchment paper, and press down with bench scraper to further smooth top and square edges. Let stand overnight. Using excess parchment as handles, remove from pan. Using a sharp knife, cut into 5 equal bars or 30 square pieces. Wrap in wax paper, and tie string around the ends. Store in an airtight container for up to 1 month.