TAMPA, Fla. -- The congratulatory phone call that Ron Guidry expected for years took place last Oct. 4, while the rest of the baseball world seemed to be focused on Aaron Judge’s 62nd home run and the passing of Roger Maris’ 61-year-old single-season American League record.

Guidry had been watching via iPhone from his Louisiana home that night, remaining tuned in as Gerrit Cole shattered Louisiana Lightning’s franchise record for strikeouts in a single season. With 257, not Guidry’s 248, now the benchmark, the 1978 AL Cy Young Award winner had a telephone call patched into the visiting clubhouse at Globe Life Field.

“I’ve been waiting ever since you put the Yankees uniform on for this moment, because I knew you were going to do it at some point in time,” Guidry told an appreciative Cole that night. “You’ve earned it.”

Those congratulations were relayed in person for the first time on Thursday, as Yankees pitchers and catchers went through their first official workout at George M. Steinbrenner Field. Cole tossed two simulated innings in a morning bullpen session, with manager Aaron Boone, pitching coach Matt Blake and Guidry -- a special guest instructor -- looking on.

“It’s always just kind of an exciting time to be back around everybody,” Cole said. “It’s always good to see Gator. We exchanged cordials and talked a bit about how cool it was for both of us, that night in Texas.”

Though left-hander Carlos Rodón is the new face in the Yankees’ rotation, Cole remains the ace, coming off a 2022 season in which he was 13-8 with a 3.50 ERA in 33 starts. An All-Star for the fifth time, Cole paced the Majors with 257 strikeouts to eclipse Guidry’s 1978 tally, but also led the AL with 33 home runs surrendered.

“I think every year, you try to evaluate what you can do better,” Cole said. “Sometimes there aren’t things that are not quite as obvious as leading the league in home runs, but you’ve got to be out there to pitch quite a bit if you’re going to. … The solo home runs really aren’t it. It’s the late ones that flip the game a little bit, or when there’s two or three runners on base.”

Said Boone: “For as good a year as it was, he faced his share of adversity. I thought one of the best things that happened for him and for us last year was, I remember a lot of the questions going into the postseason around him. He really bounced back and continued to solidify himself as one of the real aces in the sport.”

This is the fourth year in pinstripes for Cole, who signed a $324 million deal with the Yankees after the 2019 season. At Cole’s introductory press conference, managing general partner Hal Steinbrenner said that he expected the contract would produce “championships -- multiple” over its nine years.

“My biggest goal is to win a world championship for this organization,” Cole said.

So far, Cole has advanced no further than the American League Championship Series, and it hasn’t always been pretty. He quipped on Thursday that the Yankees got “waxed” by the Astros in last October’s ALCS sweep, adding, “Any time you get waxed, it doesn’t feel good, whether you’re going to the salon or you’re on the baseball field.”

Yet Cole remains optimistic in the Bombers’ chances, and Boone believes that Cole can individually take his game to even greater heights.

“There’s always another level he can go to have that Cy Young season where he finishes that off,” Boone said. “He’s always going to be in that running. He’s been an absolute workhorse. He’s so good at taking care of his body, knowing himself and knowing how to prepare 365 days a year.”

As Cole and Rodón prepare to head a stable of starters that projects to include Luis Severino, Nestor Cortes and either Domingo Germán or Clarke Schmidt, Cole said that it is his responsibility to set a strong example and lead the way.

“I just want to make this a really great learning environment and competitive environment for all of our pitchers and players, and represent Hal and the Steinbrenner family and organization well,” Cole said. “I just kind of take those things in every facet of my job. That’s certainly a big part of it, and I take it seriously.”