Twenty20 captain Broad took a hat-trick as England cruised to a comfortable 46-run victory over a New Zealand XI in a T20 warm-up on Tuesday morning, looking fully back to fitness after injuries cut short his tour of India.
With series at home and abroad against New Zealand to come before England defend the Ashes on home soil, Cook is eager for Broad to be fit and firing. Cook told Sky Sports News: "He's a very important player for us. It was great for me to see him back playing."
He continued: "He had a tough tour of India where it was just a case of trying to get him on the park, he had a few niggles and was trying to play through niggles, but it's great that he's now fit and leading the Twenty20 side out in New Zealand.
"He needs a few overs under his belt but once he gets them he'll be ready for the T20s, the one-dayers and the Tests to come afterwards.
"He's a massive player for us, he's delivered in big matches for us and before such a big summer and winter coming up, we need all our players fit and available for that."
Jos Buttler recorded his maiden England 50 in just 21 balls, and Cook believes he is just part of a group of young players who can make their mark this summer, also singling out Joe Root.
"Joe has had a great rise, playing in all three formats, and the way he has handled himself in the Test match in Nagpur, playing under great pressure, and in the one-dayers against India, he looks the real deal at international level," he said.
"Jos has come in and, as we've seen him doing for Somerset at the end he's a very destructive hitter.
"That's translated into the international game now and it's great to see English cricket producing these players and seeing them come into the team."
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