In a medium saucepan over medium-high heat, cook strawberries and 1/4 cup sugar, mashing with a potato masher or back of a wooden spoon, until strawberries release their juices, about 1 minute. Bring to a boil and cook, maintaining a boil and stirring occasionally, until thickened, 7 to 9 minutes.
Remove saucepan from heat, stir in lemon juice and 1 teaspoon vanilla, and strain through a fine-mesh sieve set over a heatproof bowl, pressing on solids to get all juices and puree (you should have about 1/2 cup puree). Refrigerate until completely cool, about 1 hour.
Meanwhile, in a large heatproof bowl, cover cashews with boiling water to a depth of about 1". Let soak until cashews are softened, about 30 minutes. Drain well and transfer to a blender. Add almond milk, coconut cream, salt, and remaining 1/2 cup sugar and 1 teaspoon vanilla. Process on high until smooth, about 2 minutes.
Pour cashew mixture into an 8"-by-8" baking dish and stir in cookies. Drizzle strawberry mixture over top. Cover and freeze until firm, at least 6 hours or up to overnight.
Let soften at room temperature 10 minutes before scooping. Serve topped with more crushed cookies.