I would suggest The Shia Revival by Vali Nasr. It's way too simplistic to say that Islam+Zoroastrianism=Shia Islam, but certainly there is some truth to that.

Simply Shia Islam since the Safavids has been largely synonymous Iranian/Persian Islam. Just like European Christianity held on to A LOT from European Paganism, all forms of Iranian Islam held onto a lot of Zoroastrianism.

The first thing we have to remember is that Iranians/Farsis/Persians have been a great civilization for an extremely long time and have an extremely rich cultural history. During the Muslim expansion (mid 600s AD) Iranian elites lived in cities, recited poetry and were very aware and proud of their cultural pedigree. The Arab invaders who conquered Iran and brought Islam, were basically bad-ass, barbarian nomads who were really good at winning wars and had one really good, really new book. They also spoke a TOTALLY different language than the Iranians. While Iranian is an indo-european language Arabic is a semitic one.

This made assimilation pretty hard, and even after Zoroastrianism was crushed and most Persians became Muslim there was still underlying tension, that was made worse by fact that Arab invaders were setting themselves up as overlords and discriminating against Persian Muslims, imposing Arabic as the official language and generally denigrating Persian culture.

Despite the fact that Islam was to a large extent forced on the Persians, by the 750s they began using Islam as a way to assert their identity and resist Arab oppression. By the mid 700s persian elites were largely back in control of Iran. These elites and the scholars, artists and philosophers they funded had a huge impact on Islam.

As Bernard Lewis said:

Iran was indeed Islamized, but it was not Arabized. Persians remained Persians. And after an interval of silence, Iran reemerged as a separate, different and distinctive element within Islam, eventually adding a new element even to Islam itself. Culturally, politically, and most remarkable of all even religiously, the Iranian contribution to this new Islamic civilization is of immense importance..... In a sense, Iranian Islam is a second advent of Islam itself, a new Islam sometimes referred to as Islam-i Ajam. It was this Persian Islam, rather than the original Arab Islam, that was brought to new areas and new peoples: to the Turks, first in Central Asia and then in the Middle East in the country which came to be called Turkey, and of course to India."

This "Persian Islam" (which was still Sunni) used lots of Zoroastrian symbolism in it's art, and even went so far as to display pictures of the Prophet and his family, which is unheard of in most Islamic art and probably stems from Zoroastrian artistic traditions. Persian Islam historically has also had a more hierarchical, organized Ulema/Clerical system than traditional Arab Islam has, which some scholars believe is an echo of the powerful Zoroastrian priestly class (this is more controversial though.)

Fast forward almost 1000 years to the 1500's and a Sunni-born Persian warlord named Ismail I was able to unite almost all Persian speaking people into the Safavid Empire. He was big on defending Persian identity against encroaching invaders. (now mainly Turks and other Muslim steppe people) In order to give himself legitimacy, give his new Persian empire a separate identity and possibly because he had a genuine conversion experience, Ismail converted to Shia Islam and forced all his Sunni subjects to do the same.

Importantly he brought many Levantine (ie. Not Iranian) Shia Ulema to teach Shia law and theology. That being said, since Ismail Shia Islam's center of gravity has always been in Iran. Since Iranian culture was so impacted by Zoroastrianism, there are influences in Shia worship.

However, keep in mind calling a practicing Shia a Zoroastrian or implying that their religion is half Zoroastrian is very insulting to them, as they see their deen as original, unadulterated Islam.