Hi Hadar! As a big fan of podcast who has been benefiting a lot from that when it comes to languages learning, I'm very happy to come across this post, and would like to share with you some podcasts I have been listening for years!
FYI: I'm a Chinese native speaker, my second language is English, and I've been learning Japanese, Korean, German and Norwegian. Here I will list some for Korean and Chinese.
Podcasts:
Part 1- Korean Learning
1, Talk to me in Korean (Best one I have found so far for both beginners and advanced learners)
2, Learn Korean with David (A very useful platform to learn basic Korean words and phrases with perfect timing)
Part 2 - Chinese Learning
1, Himalaya FM (A platform for creative audio content in Chinese, you might need to find the topic interest you most)
2, 糖蒜女子脱口秀 (Advanced Level )
3, Round Table 圆桌会议 (Bilingual in Chinese and English )
(Those are based on contents more than languages learning as I'm a native speaker, other fellow Chinese learner might have better ideas than I do)
Tips:
1,You may find it's almost impossible to catch up at the beginning, which is very normal it happed to me as well, as our sub-conscientious brain is faster than your conscientious brain, listening is basically harder even your reading and writing are already good, so you might need more patience and dedication when you start this learning process.
2, Find the content that interests you so you can listen to it everyday, in other word, find a solution that is sustainable for you, is very important no matter if you choose podcast or cartoon......
Good luck!