Redskins quarterback Kirk Cousins messes up GM Scot McCloughan' s hair, asking "How do you like me now? " after their win over the Green Bay Packers at FedEx field. (Jonathan Newton/The Washington Post)

Whenever Kirk Cousins talks about his quest to establish himself as the franchise quarterback of the Washington Redskins, he mentions the learning process, and how he values experience as part of his growth.

With his team playing the Green Bay Packers, the same team that eliminated Washington from the playoffs just 10 months earlier, Cousins on Sunday showed his growing depth of knowledge, making one big throw after another. With another 300-yard game (his fifth of the season) and three more touchdown passes, Cousins led Washington to a 42-24 victory over Green Bay and improved to 6-3-1.

Last January, Cousins looked overwhelmed in the second half as he and the offense failed to build on an 18-17 lead and eventually fell, 35-18.

But this time around, Cousins produced his biggest throws.

Cousins completed 21 of 30 passes for 375 yards and the three touchdowns, no interceptions and a season-high 145.8 passer rating. He completed 7 of 10 third-down pass attempts.

As he came off the field, the quarterback saw General Manager Scot McCloughan entering the tunnel. “How do you like me now?” said Cousins, who is playing on a one-year, $19.95 million franchise tag this season, hoping to earn a long-term deal.

Asked later about his remark to the GM, Cousins was coy. “I’m always trying to prove myself and I’m always going to be evaluated as long as I play this game,” Cousins said.

Cousins proved plenty in the second half, shining when the pressure was heaviest. On third and five from the Green Bay 49, Cousins fired a 28-yard strike to tight end Jordan Reed to put his team in scoring position. The drive culminated with a field goal to give Washington a 16-10 lead.

Later, on third and 11 from the Green Bay 44 with 2:07 left in the third quarter, Cousins hit Jamison Crowder in stride for a 44-yard scoring pass down the center of the field.

He was far from done. Just 34 seconds into the fourth quarter, he found Pierre Garcon for a 70-yard bomb that gave Washington a 29-17 lead, his longest touchdown of the season.

“Kirk is always getting better and better the more he plays,” Garcon said. “We know what he’s capable of. It was good to see him have a big game and good to see us make the plays for him.”

The Packers kept answering. But so did Cousins. With 4:44 left in the game, Cousins found Crowder again, completing a 53-yard pass to the slot receiver, who was tackled at the 1-yard line. Rob Kelley scored one play later.

Sunday night’s performance continued a second strong season for Cousins, one that could result in the deal the quarterback seeks. Since his career-high 458-yard passing day in the tie against Cincinnati, the quarterback has played with greater confidence and aggression.

He has limited mistakes and displayed greater poise under pressure.

Cousins has put up numbers all year. After the first half of the season, he was second in the NFL in passing yards. However, he was only middle of the pack in touchdown passes. But the quarterback has found his receivers for scores more frequently in the past three games, in which he has passed for 1,095 yards, seven touchdowns and only one interception .

Cousins’s first-half play had a tentative quality to it, especially in the red zone. His second-half surge resembles the stretch run he put together last season, when he threw 19 touchdowns and only two interceptions while leading his team to an improbable NFC East title thanks to a four-game win streak.

The Redskins have won six of their past eight games, and two straight. It’s no coincidence that the emergence of Kelley has helped the Redskins find greater balance on offense, and opened up the play book for Cousins.

But Cousins’s confidence has shown through particularly in the red zone, where Washington ranked next to last in the league in the first half of the season.

The quarterback’s next challenge? Can he stay hot on a short week, because the Redskins on Thursday will play the division-leading Cowboys in Dallas.