Preheat the oven to 350 degrees F. Toast the almonds on a baking sheet until golden brown, about 20 minutes, and then roughly chop.
Whisk the egg whites in the bowl of a stand mixer fitted with a whisk attachment on medium speed for about 3 minutes, and then turn up the speed to medium high until the egg whites are at stiff peaks. Add in 1/3 cup of the sugar a little bit at a time and continue beating until the egg whites are glossy, thick, and hold their shape, about 5 minutes. Fold in the almonds.
Lower the oven temperature to 225 degrees F. Line a baking sheet with parchment paper. Drop about 1/3 cup mounds of the meringue onto the baking sheet about 4 inches apart, and then spread each one to form a 3-inch circle using a spoon. Bake for 3 hours, and then turn off the oven, leaving the meringues to cool gradually inside until dry to the touch, another 2 to 4 hours.
Combine the strawberries and raspberries and divide evenly between 2 bowls. Sprinkle 1 tablespoon of the sugar into each bowl and toss. Let sit 30 minutes, and then mash the berries in one of the bowls with a fork until it resembles a chunky puree, leaving the berries in the other bowl whole.
Whip the heavy cream and 3 tablespoons of the sugar with a whisk or hand mixer until soft peaks form. Fold in the berry puree.
To serve, put a meringue circle in the bottom of a shallow bowl, and then top with the berry whipped cream and the macerated whole and cut berries. Alternatively, break up the meringue into bite-size pieces and layer with the whipped cream and berries in a glass bowl or cup like a trifle. Eat your Eaton Mess within 30 minutes of assembling or the meringue can lose its crunch.