Is there any school or institution dedicated to teaching Jhana?
Ven. Pa-Auk Sayadaw teaches both Samatha and Vipassana meditation. First one develops Jhanas and then one can progress to Vipassana if wanted.
Here is a description from the website of Pa-Auk Forest Monastery:

&quot;The meditation taught at Pa-Auk Tawya is based on the instructions by The Buddha as found in the Tipiṭaka (the Pāli Canon) and its commentaries.
In brief, the main practice is to begin with Samatha (tranquility) meditation, which is to develop absorption concentration, also called jhāna. A yogi (meditator) is free to choose any of the forty Samatha subjects as taught by The Buddha. In Pa-Auk Tawya, most yogis develop jhāna with mindfulness-of-breathing (ānāpānassati).
Having developed Samatha, the yogi may proceed to practise Vipassanā (insight) meditation&quot;.