Business Insider published a piece last year de-bunking the ice cream story, so I won't spend much time on it here beyond saying that if the news you are reading doesn't link back to the original source, be wary. "Scientists say" doesn't cut it.
Even in articles that link back to the original source or interview the original author, like the Telegraph piece above, journalists may choose to focus on only a portion of the results. That, combined with headlines' dual purpose as clickbait, leads to titles like "Chocolate Cake Breakfast Could Help You Lose Weight".
Let me tell you the real story.
The point of Jakubowicz, Froy, Wainstein and Boaz's article was not to test if eating cake for breakfast was good for you. In fact, they only studied people who were overweight or obese. If you are not in one of those categories, the findings of the study may not apply to you. In general, though, they were interested in how the timing of food intake would affect people's weight loss, as well as other biochemical factors like ghrelin levels and psychological factors like appetite and craving scores.
So, what did they do? Well, they assigned people to either a low-carb (300 calorie) breakfast condition or a high-carb (600 calorie) breakfast condition. Both conditions also had a good amount of protein (30 and 45 grams, respectively) and yes, the high carb condition did include a dessert.
In fact, the dessert factor kind of throws the results from the study into question. Why? The researchers took great care to make sure that all participants ate the same total number of calories per day to make sure they were manipulating the timing and not the total amount of food. This is how good experiments are designed. We isolate factors so that we can be sure whatever happens is due to what we think it is. So far as I can tell, however, the low carb breakfast group NEVER received dessert, not even with their larger evening meal. This means that we won't be able to tell if the difference between the high carb breakfast and low carb breakfast groups were because of the size of their breakfast or whether they received dessert. The Telegraph would like you to believe the latter, but that's because people like to click on pictures of chocolate cake.
What were those results? Well, the authors found that both groups showed similar weight loss at the end of treatment, but very different results at follow-up. Four months after the treatment ended, the researchers found that those in the high carb breakfast group had continued to lose weight, while those in the low carb group regained most of the weight they had lost. The authors concluded that having a large breakfast high in carbs and protein can help prevent weight regain. Notice how they said nothing about chocolate cake.
Does this mean you should never eat chocolate cake again? Of course not. What is does mean is that if we want to establish whether eating sweets at breakfast can help curb cravings later, we need to run a study where both groups eat large, high carb and protein breakfasts, but only one of them receives some of those calories in the form of a dessert. I know which group I'd want to be assigned to.