Intention regarding what one plans to eat affects the need for additional berachot in two different ways, and at two different points during the eating process. After briefly discussing the principles of each, we will see where your case fits in.
Intention when one begins to eat: If, when one recites a beracha, he has in mind to eat several foods, the beracha covers other foods that one would make the same beracha on, including those that are not in front of him or those that he has no specific plans to eat.[1] If one intends, at the time of the beracha, to eat only a certain food or foods, then he needs to recite a new beracha before eating other foods, even of the same category.[2] When one did not give the matter thought, then, according to most poskim, he does not make another beracha. This is because we assume that, normally, the extent of one’s eating is open-ended.[3] However, the Rama[4] says that, to avoid doubt, it is best for a person to have in mind to cover everything that he might later decide to eat with his beracha.
Intention when one finishes eating: The gemara, in different places, discusses acts that signal the end of a meal: 1) removal of the small table at which a person was eating;[5] 2) rinsing one’s hands with mayim acharonim;[6] 3) announcing that the group is ready to recite Birkat HaMazon.[7] The key issue is hesech hada’at (‘removal of thought’); by performing an action that indicates that one is preparing for the berachot that follow eating, he shows he has ‘removed his mind’ from the eating that was included in the original beracha. Thus, to continue eating, he must make a new beracha.[8] The Mishna Berura[9] says that a clear thought that one has finished eating constitutes hesech hada’at, even if the thought has not been verbalized. Some Rishonim[10] distinguish between different types of eating: If one was drinking or having a snack,[11] then verbal or mental hesech hada’at suffices. However, if one was eating a meal,[12] then only mayim acharonim constitutes a break. The Bi’ur Halacha[13] says that it is difficult to decide between the different opinions and, therefore, urges one to avoid having cognitive hesech hada’at followed by a change of mind during a meal.
Let us now return to our case. If one had decided to have a snack of a single cookie, then the beracha would never have applied to other foods. However, once his intention was open-ended enough to apply to other foods, only positive hesech hada’at removes the beracha’s effectiveness. All of the poskim we have found discuss hesech hada’at from the perspective of the present. (For example, see the language of the Rambam and the Mishna Berura.[14]) In other words, one says to himself, “I no longer plan to eat,” which is equivalent to actively preparing for Birkat HaMazon. There is no halachic precedent for a delayed or planned hesech hada’at (i.e., “After one more cookie, I will have stopped eating.”).
Thus, if, after finishing the cookie, you continued to think that it was indeed the last one, then you had hesech hada’at at that time. As you are presumably referring to a snack, you would have needed a beracha before eating more. However, if your resolve to stop eating wavered before you finished eating the originally intended amount, you could have continued without a new beracha.