Climbing a long hill is all about putting out a steady power for an extended period. If you don't have big hills nearby find a flat section or loop where you can do steady efforts of at least 20min. The elevation profile you provided might be hard to maintain a steady effort if the downhill sections are fast.

When you say you 'immediately run out' as soon as you hit a big climb that's because you are starting out too hard. If you're used to short hills, the effort you put out on short hills will be much higher than what you can sustain for a long climb.

If you have a HRM focus on keeping your HR steady for 20min. That may mean you go into a lower gear than normal for the short uphlils and pedal harder than you're used to on the downhills. You need to figure out the HR you can sustain for an extended period of time. A powermeter would be helpful if you can get access to one.

I do most of my riding in flatish areas with the hills only between 50-100m. I have to ride for 2 hrs to get to a 10-15min hill. But I do have access to flat areas where I can ride at a steady power for an hour. I did my first big climb of the year yesterday (900m) and while I suffered going up, it didn't feel much different than a steady 1hr ride on the flats.