Microwave the chocolate in a small bowl for 30 seconds, stir, then microwave another 30 seconds and stir again. Repeat (if necessary) until melted and smooth. Add the chopped Cheez-Its to the chocolate and toss until coated. Remove and spread on waxed paper. Put in the freezer for 10 minutes or until hardened.
Add the sugar, eggs, cocoa powder, and milk to a blender and blend. Pour into a microwave-safe bowl and microwave on high for 1 minute. Stir, then microwave for 30 seconds; repeat 2 more times until the mixture is slightly thickened. (Don't be tempted to microwave longer than 30 seconds in a row after the first minute or you'll end up with scrambled eggs.) Whisk in the cream and pinch of salt. Pour onto a clean cookie sheet (with sides) and chill in the freezer for 20 minutes. Remove and pour into the ice cream maker, following the manufacturer's instructions. Add the chocolate-covered Cheez its to the ice cream during the last couple of minutes in the ice cream maker — after the mixture has thickened to soft serve consistency. Remove ice cream when desired consistency is reached and serve or freeze immediately.