Brook's dashing 109 helped lay the foundation for England's 241-run win over the West Indies at Trent Bridge, a result that put the hosts 2-0 up in a three-match series ahead of this week's finale at Edgbaston.
Brook has now scored five Test hundreds, with his first four centuries scored abroad against Pakistan and New Zealand.
Brook's average of 62.54 after 23 innings is the highest since Australia hero Don Bradman, widely considered to be Test cricket's greatest batsman, among players with over 1,000 runs in the format.
"I've only just started," said Brook. "That could definitely fluctuate either way. I've not even played 25 innings in Test cricket yet so I won't be getting ahead of myself.
"I'll just keep enjoying playing Test cricket. Hopefully, I can keep it that high but if not, so be it."
At Trent Bridge, Brook shared a stand of 189 with Yorkshire team-mate Joe Root, who also scored his first Test century of the season.
Brook, whose 363 runs against Australia last year, helped draw the Ashes, said while he was glad to learn from Root, he was also determined to stay true to himself as well.
"I want to be my own batter, I want to be Harry Brook, not anybody else."
But he added: "Rooty has just gone eighth in the all-time Test runs list, so I'd be stupid to not be tapping into his cricket knowledge.
"I was glad to get it (the hundred) on the board, being my first in England.
"I was nearly getting to the spot where I thought, 'God, I need a hundred in England'. I didn't get a big one in the Ashes last year, but I was happy with my performances."
Brook withdrew from the Indian Premier League earlier this year following the death of his grandmother, having previously pulled out of England's five-Test tour of India in January due to personal reasons. He later revealed his grandmother was "ill and didn't have long left".
And it was his grandmother Pauline, one of his biggest supporters, who was uppermost in Brook's mind when he reached three figures in Nottingham.
"It was the first (century) with family there and obviously loads more English fans as well, it was a very nice moment.
"I'm not a massive celebrator at a hundred, I just try to soak it all in. I did it all for my grandma.
"As soon as I got it, it was just like, 'Yes, a hundred'. But a couple of moments later I got a bit emotional inside, I just didn't show it. I was thinking about her."
England have four Tests left to play this season, with Sri Lanka arriving for a three-match campaign starting in August.
And for Brook, an in-demand multi-format player, Test cricket is still the pinnacle.
"I want to play every Test match I can for England," he said. "Test cricket and playing for England is my priority."
