High fat doesn't necessarily have to be excessive fat - it can just be a matter of ditching the low fat high sugar stuff for lower carb full fat versions, replacing margarine with butter, or eating fatty meats or oily fish, full fat yoghurt, using good oils or butter for cooking and sauces. Avocados, olives, and nuts (and nut oils and butters) are also good sources of oils too, to say nothing of a little piece of high (75%+) coco dark chocolate. There's nothing wrong with it -and it was the way we
used to eat before the current low fat "regime". You only need to include enough fats and oils to replace the energy you were previously getting from the carbs you're now cutting down on.
If you're type 1 you'll probably need to reduce your insulin too and there are a number of other type 1 low carbers ( and I believe also some type 2's on insuilin) who should be able to advise and help with this aspect if necessary.
Also have a look at some of the low carb nutritional calculators, as these can help you get your proportions of carbs. protein and fats correct for your height, weight, and other specific requirements - mainly to lose, maintain, or even gain weight. This is usually a matter of balancing your fat needs after determining the other two. Try
http://www.phlaunt.com/diabetes/DietMakeupCalc.php, but there are others - some of which need much more data!
I know someone who whips some cream and adds instant coffee granules and stevia, and eats it from a bowl - she calls it her coffee chiffon pudding, but I haven't tried it as it seems a step too far on the fats side.
I do something similar but generally with a mix of soft or cream cheese with my cream and some sort of flavouring and sweetener - erythritol in my case. So coffee granules and chopped walnuts, cocoa powder with maybe peppermint or orange essences, or ground ginger, cinnamon & nutmeg to go with a low carb ginger biscuit, or soft cheese with coconut butter and zest and juice of a lime or two. A small bowl is plenty and it's not actually any worse than eating real ice cream!
Robbity