What is the proper bracha to say on pizza and bagels?
The Shulchan Aruch says in סימן קס"ח סעיף י"ז anything that was baked in the oven with meat, fish, or cheese on top of the dough, the proper bracha to say is hamotzi.
The Mishnah Berurah says that even if the person didn't think of the food as a meal (קביעות סעודה), they must still say hamotzi on it. That person cannot think of it as bread stuffed with fruits and spices, which a person would normally not say hamotzi on it unless they thought it was a meal. People tend to think of bread stuffed with fruit and spices as a dessert since it is sweet. On the other hand, people normally eat bread that is stuffed with meat, fish, or cheese when they are hungry and want a meal — just like any other bread which people eat with meat such as a sandwich.
Furthermore, the Mishnah Berurah says if the bread is made in small pieces like crackers, and minced meat is inside it, and it is for a dessert, it is like the bread with stuffed fruit and spices, and you would say mezonot on it.
The Bracha on Pizza
Based on this ruling, the blessing on pizza made with dough that was kneaded with fruit juice is still hamotzi since pizza is normally eaten as a meal. However, if a person is in a place where pizza is served as dessert, and the dough is kneaded with fruit juice, then the pizza is mezonot. This is also the ruling of הגרשז"א and the ruling of Rabbi Yitzhak Abadi from Lakewood in his book Or Yitzhak in סימן ל"ו.
The Bracha on Bagels
The Shulchan Aruch says in סימן קס"ח סעיף י"ד boiling a bread in water and then baking it in the oven is considered a complete bread and the proper bracha is still hamotzi. Based on this סעיף of the Shulchan Aruch, bagels are hamotzi since they go through this process. A certain Chacham ruled in his community that bagels should be mezonot and not hamotzi since the bagles are edible after the boiling. However when we look in the books of the Rishonim, we see a different picture. All of the Rishonim except the Ramban have a qualm about the edibility of the boiled bread before it is baked. The fact that the Shulchan Aruch doesn't differentiate between the edibility of the bread at different stages of the process shows that it does not matter, and there is no place to say סב"ל (the concept of disagreement regarding Brachot inducing leniency).
Since the Ramban opinion is rejected by the overwhelming majority of the Rishonim, the custom is to say hamotzi on bagels and not mezonot. This conclusion is also reached by the Chazon Ish in Or Hachaim סימן כ"ו. It says that any dough that was cooked or fried and then baked is considered complete bread and therefore the round bread we call bagels that are dipped in boiling water and then baked afterwards, is considered a complete bread, and therefore we say hamotzi on it.