Along the way, Egan sets a goal for himself: to get enough stamps in his pilgrim passport to earn a special seal from the Vatican at the end of the journey. Considerable energy builds around the lengths he goes to to get those stamps. When he finally lands the hard-won certificate, he says: “It’s official. I know how the Scarecrow felt when he got his brain.”

“A Pilgrimage to Eternity” is also a stunningly comprehensive history of both Christianity and Western Europe. It’s all here: from St. Maurice, “believed to be ‘the first black saint’” (wrote Henry Louis Gates Jr.), and the 1,500-year-long uninterrupted prayer at the abbey named for him; to the 1518 Treaty of London forever outlawing war between Christians (it lasted “barely two years”); to Mencken on Puritanism: “The haunting fear that someone, somewhere may be happy.” In fact, there’s so much history that the plot can sometimes feel like an excuse to get the background in, though one hardly complains; Egan is so well informed, he starts to seem like the world’s greatest tour guide. You follow along as much to hear him talk as to see the sights. It feels as if there’s nothing he hasn’t digested for the reader, and his extraordinary reliability is reminiscent of that of the monks he describes so evocatively throughout the book.

Egan doesn’t shy away from contentious subjects. He calls for more women in the church’s hierarchy. “The desire among women to be a guiding part of this faith is great,” he writes. “There are more than 50 percent more nuns and sisters in the world than priests.” He’s sick of the church’s censorious attitude about sex — little basis for which can be found in Jesus’ teachings — and harbors a healthy skepticism about Mary’s perpetual virginity and Jesus’ celibacy. He sees misogyny in this history, and in the revisionist denigration of Mary Magdalene, and traces this thread from St. Paul — an “early celibate” — to SS. Jerome and Augustine, who preached celibacy after long careers of debauchery, and to St. Benedict, who “feared sex so much that whenever he was aroused he threw himself into a patch of nettles or a bed of thorns.” Of the 1968 Vatican encyclical against birth control, Egan writes that it “is almost universally ignored by Western Catholics — and has little basis in the philosophy of Christ.”

Egan also turns a critical eye on those who treat refugees poorly. For instance, he describes how the police in St.-Omer, France, “fired tear gas at volunteers” who were distributing food and clothing to refugees. Representatives of Secours Catholique, the charity behind the effort, pleaded, “Didn’t Christ say we have an obligation to help ‘the least of these brothers of mine’?” The authorities’ response: Such assistance would only encourage the refugees to stay. Egan writes, “A religion whose leaders once called on followers to wage savage war against faraway cities held by people of a different religion now fights to feed and protect forsaken members of that same faith from those same faraway cities.”

After traveling through England, France and Switzerland, bedraggled and untouched by strangers, Egan finally receives a hug from a woman in Italy. She is no longer a Catholic — but she still asks Egan to say a prayer for her when he sees Francis. “I like this pope,” she says.

The woman would never know if Egan failed to utter that prayer, but he keeps his promise at a Mass at St. Peter’s Basilica. Of course he does, you think at the end of this marvelous account. Reading it, you feel yourself in the presence of goodness — the kind you might simply have to decide to believe in.