1. Place crushed cookies in a large bowl; stir in butter until thoroughly combined. Press mixture into the bottom and partially up the side of a 9-inch springform pan. Refrigerate until ready to fill.
2. Place raspberries, 2 tbsp of the sugar and the cornstarch in a small saucepan. Over medium heat, bring to a gentle simmer; cook 10 minutes, stirring occasionally. Strain and let cool.
3. Stir 1/3 cup of the raspberry puree into softened ice cream and swirl. Spoon into springform pan and level off with a small spatula. Freeze overnight.
4. Remove cake from freezer and let stand at room temperature for 10 minutes. Toss peaches with remaining 1 tbsp sugar; fan over top. Wrap sides of pan in a warm damp towel. Run a spatula around sides; carefully remove side of pan.
5. Garnish with toasted almonds and serve with remaining raspberry puree.