Chris Stapleton laughs at the idea of having had time to process the past year.

“I really haven’t had much time for anything,” says Stapleton, calling from his Nashville home. “We’ve been on this rapid growth path, so there’s a little catching up to do.”

That’s a Stapleton-esque understatement. In the past year, the former SteelDrivers frontman has gone from a respected traditional country artist playing theaters to one of music’s biggest stars, whose current tour stops at Pennysaver Amphitheater in Farmingville on July 14 and Forest Hills Stadium on July 23 — all thanks to his Grammy-winning breakthrough album “Traveller” (Mercury Nashville) and some high-profile appearances.

Stapleton’s roll began in November at the Country Music Association Awards that he says was one surprise after another. “I was shocked we even got nominated, let alone going on to win,” said Stapleton, who ended up getting three awards, along with performing a stunning duet with Justin Timberlake on “Tennessee Whiskey.” “Those things had all kind of compounded that evening and it continued to snowball.”

That snowball took “Traveller” all the way to No. 1 on the album charts for two weeks and turned the 38-year-old touring veteran into an “overnight sensation.” “It’s the power of television,” Stapleton said. “My meat and potatoes is going out and playing live. People hear the music and they want to play it for their buddy and that process continues. This just happened on a much larger scale.”

Stapleton said he and his band — which includes his wife, Morgane, on backing vocals — may try out some new songs at his area appearances. However, they won’t get down to recording new music until November for a spring 2017 release. He says his approach for the new songs will be similar to those on “Traveller,” adding, “It ain’t broke.”

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He plans to enjoy all the new venues on this tour, including playing Forest Hills Stadium where Bob Dylan famously played the controversial summer he went electric.

“We get to play these great historic venues that are like new badges of honor to wear,” Stapleton said, jokingly adding that he would like to do something to commemorate playing Forest Hills.

“Maybe I’ll do an all-ukulele set,” he said.