The young Magpies make the short trip to the Daren Persson Stadium to face the Northern League Division One outfit after progressing into the last four by defeating Ashington via penalties, following a 2-2 draw at Woodhorn Lane.
Brookwell, who joined the Magpies' youth set-up from Liverpool in the summer of 2020, is determined for Newcastle's second-string to advance into the final, which will be staged at St. James' Park.
The Wigan-born defender, who is capable of playing in midfield, told nufc.co.uk: "We don't play in that many cup competitions so the ones we are in, we want to go as far as we can. We want to test ourselves against men and if we can show we can win those games, it can only help us.
"Any game at St. James' Park is good but with it being a final, it adds that extra bit more on. To win a trophy there is something everyone in the squad wants to do.
"We played against Ashington in the quarters and, as a team, we learnt a lot that night in being 2-0 up but taking our foot off the gas. It cost us and we just ended up going through on penalties.
"I'm sure if we went 2-0 up in this game, we won't want the same thing to happen and take our feet off the gas.
"It's good to be facing senior opposition. It's something different - something to look forward to. The atmosphere is usually good for these matches so we're excited.
"We're expecting a few fans there but the lads are looking forward to showing them what we can do."
United's second-string suffered a heavy 6-1 defeat against Premier League 2 Division Two leaders Fulham on Monday night but Brookwell is hopeful Newcastle's youngsters can bounce back swiftly ahead of facing the Robins.
Brookwell, who scored on his under-23s debut against Middlesbrough in September 2020, believes the quick turnaround in fixtures can benefit the squad as they bid to reach the Northumberland Senior Cup final for the first time since the 2017/18 campaign.
"It was a bad night for us against Fulham", the teenage centre-back added. "We know we have to be better, although we'd been on a good run. A blip can't turn into a poor, poor run of games so we need to nip it in the bud. The best way to do that is by winning on Thursday night.
"It's good to be play straight after a defeat because you have less time to dwell on the Fulham game and gives us a chance to show we're better than what we showed on Monday.
"We've had a good season and we need to make sure that was a one-off. We want to win this trophy and when you have a trophy at the end of the season, it looks good so we're very determined."
