One who eats ice cream – whether he eats dairy ice cream or parve ice cream – first recites the Beracha of "She'hakol." What is less clear is whether Halacha treats ice cream as a solid food or a liquid, as issue that yields several important ramifications. For one thing, when a person drinks wine with other beverages, the Beracha of "Bore Peri Ha'gefen" that he recites over the wine covers the other beverages, as well. Hence, if we treat ice cream as a beverage, rather than a food, then a person who eats wine with ice cream should not recite a Beracha over the ice cream, as the Beracha recited over the wine covers the ice cream.
This question will also affect the case of one who eats ice cream for dessert during a bread meal. The Beracha of "Ha'mosi" recited over bread at the beginning of the meal covers all beverages drunk throughout the meal, until Birkat Ha'mazon, regardless of a given beverage's function or context. Therefore, if we view ice cream as a liquid, then one would not recite a Beracha over ice cream when he eats it at any point during a bread meal.
As for the final Halacha, Rabbi Moshe Stern of Debereczyn, in his work Be'er Moshe (vol. 1, 11:2), rules that Halacha indeed treats ice cream as a liquid, and not as a solid, and thus it is covered by the Beracha recited over bread or the Beracha recited over wine. This view is codified as well by Hacham Yishak Yosef in his work Kol Torah, in the name of his father, Hacham Ovadia Yosef. The work "Ve'zot Ha'beracha" (p. 100) likewise cites this ruling in the name of several leading Halachic authorities.
It should be noted that as is the case with most foods, if a person mistakenly recited the Beracha of "Bore Mine Mezonot" over ice cream he has nevertheless fulfilled his obligation. There is a general rule in the laws of Berachot which establishes that one who mistakenly recited "Mezonot" over any food has fulfilled his obligation, except if he recited this Beracha over water or salt. The reason for this Halacha is that all foods except water and salt have the quality of "Mezin" – they provide nourishment – and can therefore be said to be included under the term "Mezonot," which refers to nourishing foods. (See Birkat Hashem, vol. 3, p. 157.) Thus, even though ice cream is treated in Halacha as a beverage, it nevertheless falls under the category of "Mezonot" in that one who mistakenly recited "Mezonot" over ice cream need not then recite "She'hakol." This is the explicit ruling of Hacham Yishak Yosef, citing his father, in his work Kol Torah (p. 49).
Summary: One who eats dairy or parve ice cream must first recite the Beracha of "She'hakol," though, as with most foods, if he mistakenly recited "Mezonot" he has fulfilled his obligation. If one eats ice cream with wine or as part of a bread meal he does not recite a Beracha, since the ice cream is covered by the Beracha recited over the wine or the Beracha recited over the bread.
