In a saucepan, combine chopped peaches, lemon juice, brown sugar, cinnamon, and nutmeg over medium heat. Cook for 10-15 minutes until softened. Stir frequently and thicken with cornstarch mixed with water before cooling.

Preheat oven to 350°F (175°C). Mix flour, brown sugar, cinnamon, and salt, then cut in butter until crumbly. Spread on baking sheet and bake for 10-12 minutes, then cool.

Line two baking sheets with parchment and prepare a macaron template underneath. Have mixing bowls and a mixer ready.

Heat sugar and water in a saucepan until dissolved. Whip egg whites to stiff peaks. Pour in sugar syrup while mixing, then continue to whip until glossy.

Sift almond flour and powdered sugar, then fold gently into the meringue until smooth.

Divide batter if using different colors. Fold in gel food coloring to achieve the desired peach hue.

Using a piping bag, pipe onto prepared sheets with space in between. Tap vigorously to remove air bubbles and let rest for 30-60 minutes.

Preheat oven to 300°F (150°C) and bake shells for 15-20 minutes until firm and smooth on top.

Cool macarons, then pipe frosting on one shell, fill with peach jam, and sandwich with another shell.