Add strawberries, raspberries, and thyme. Remove from heat. Let mixture steep, covered, stirring occasionally, for 30 to 45 minutes, or until desired flavor is reached. Strain liquid through fine mesh strainer, pressing on berries with a wooden spoon to remove juice. Refrigerate while rosé freezes.
Scrape frozen rosé into blender. Add berry liquid, lemon juice, stevia (if desired), and ice (if desired); cover. Blend until smooth. Freeze mixture for 30 minutes before serving. Reblend quickly.