In a small saucepan over medium heat, combine chopped peaches, lemon juice, brown sugar, cinnamon, and nutmeg. Stir continuously for about 5-7 minutes until bubbling. Mix cornstarch with water to create a slurry, add it to the peaches, stirring until thickened, about 2-3 minutes. Set aside to cool completely.

Preheat the oven to 350°F (175°C). In a mixing bowl, combine flour, sugars, and spices. Cut in softened butter until the mixture resembles coarse crumbs. Spread on a parchment-lined baking sheet and bake for 10-12 minutes until golden. Allow to cool completely.

Before starting, ensure all equipment is grease-free. Preheat the oven to 300°F (150°C). In a double boiler, whisk egg whites and granulated sugar until glossy and fluffy, about 4-5 minutes. Gently fold in sifted almond flour and powdered sugar. Divide the batter, coloring one half for a peach hue.

Line baking sheets with parchment paper, using a template for sizing. Transfer batter to piping bags and pipe rounds, spacing evenly. Let rest for 30-60 minutes until a slight skin forms.

Bake the macarons for 15-18 minutes, rotating trays halfway. They are done when easily lifted from parchment without cracks. Cool completely on sheets before removing.

Pipe a ring of frosting around the edge of one macaron shell. Fill the center with peach jam and sprinkle with streusel. Top with another shell, pressing gently to adhere. Repeat until all are filled and assembled.

Allow assembled macarons to sit in the fridge for 1-2 hours for flavors to meld. Serve chilled or at room temperature.