Preheat the oven to 350 degrees F. Spread the almonds out on a baking sheet and bake until light golden, 6 to 8 minutes. Set aside to cool.
Bring a medium saucepan of water to a boil. Cut an "x" in the bottoms of the peaches and tomatoes. Carefully add the peaches to the water and boil until the skins just start to peel back, about 1 minute. Remove with a slotted spoon. Repeat with the tomatoes, boiling for about 15 seconds. Set aside.
Add the basil to the boiling water and cook until just wilted and bright green, about 15 seconds. Transfer with a slotted spoon to a blender and puree until smooth. With the machine running, add the olive oil and 1/4 teaspoon each salt and pepper.
Peel and pit the peaches; peel the tomatoes. Cut both into 1/2-inch slices.
Spread the basil puree on a serving platter. Arrange the peaches and tomatoes on top. Sprinkle with the lemon juice and dollop the ricotta on top. Sprinkle with 1/4 teaspoon salt and 1/8 teaspoon pepper. Top with the toasted almonds, garnish with whole basil leaves and serve.