A basic principle in Halacha establishes that when a person eats two foods mixed together, he recites a Beracha over the "Ikar" the primary food and this Beracha covers both that food as well as the "Tafel" the subordinate food. As Hacham Ovadia Yosef discusses in his work Hazon Ovadia (Laws of Berachot, p. 285; listen to audio for precise citation), any food that is added to a dish for the purpose of adding consistency, flavor, fragrance or color is considered the "Tafel," the subordinate ingredient. Hence, one would recite a Beracha over the other food in the mixture, and this Beracha will cover the entire mixture.
Thus, for example, if one prepares a vegetable dish and adds flour as a bonding agent, to hold all the vegetables together, he would recite over the entire dish the Beracha of "Bore Peri Ha'adama," which covers even the flour. Similarly, if one adds pieces of meat to rice for flavoring, he recites over the rice the Beracha of "Bore Mine Mezonot" which covers both the rice and the meat. It should be noted that in such a case, there are two reasons why one would recite only the Beracha of "Mezonot." Firstly, as mentioned, the meat is added only as a flavoring agent, and thus constitutes the subordinate ingredient. But in addition, since the rice comprises the majority of the dish, it is considered the "Ikar" and it therefore determines the Beracha recited over the entire dish. Nevertheless, Hacham Ovadia adds, if one wishes to first eat a piece of meat before partaking of the rice, he recites "She'hakol" over the piece of meat and then recites "Mezonot" over the rice. Likewise, if one adds some vegetables to rice, he would recite "Mezonot" over the entire dish, but if he prefers to partake of a piece of vegetable before eating the rice, he recites "Ha'adama" over the vegetable followed by "Mezonot" over the rice.
In light of this principle, let us consider the case of "mehshi" and "yabra," two foods that are commonly eaten on Shabbat. Mehshi is essentially eggplant stuffed with rice and meat, and yabra is grape leaves stuffed with rice and meat. Which part of the dish do we consider the primary food the stuffing, or the exterior? And, if we consider the stuffing as the primary food, do we determine the Beracha based on the rice ("Mezonot") or based on the meat ("She'hakol")?
Hacham Ovadia Yosef, in the aforementioned work (p. 288), cites from Rav Shaul Katzin's "Peri Sadik" that it is the stuffing, rather than eggplant or grape leaves, that constitutes the primary component of the mehshi or yabra. Hence, the Beracha is determined by the majority ingredient of the stuffing: if the meat comprises the majority, then one recites "She'hakol," and if the rice comprises the majority, then one recites "Mezonot." This Beracha covers the entire dish the stuffing as well as the eggplant or grape leaves.
It should be noted that this entire discussion applies only when one eats the dish independently, not as part of a bread meal. It goes without saying that if one ate bread, then the "Ha'mosi" recited over the bread covers the mehshi or yabra eaten during the meal.
Summary: One who eats a dish of vegetables held together by flour recites the Beracha of "Ha'adama," and this covers both the vegetables and the flour. If one eats rice to which some pieces of meat or vegetables have been added, he recites "Mezonot" and this Beracha covers the entire dish. If one eats mehshi or yabra, he recites "She'hakol" if the stuffing consists mostly of meat, and "Mezonot" if the stuffing consists mainly of rice.
