Step 1: Understanding the Concept:
The question asks to identify the Satavahana king who took on the title 'eka bamhana', signifying his supreme status as a Brahmana and a protector of the varna system.
Step 2: Detailed Explanation:
The claim to be an 'eka bamhana' (the unique Brahmana) is famously associated with Gotami-puta Siri-Satakani, one of the most powerful rulers of the Satavahana dynasty. This claim is recorded in the Nashik inscription of his mother, Gautami Balasri. The inscription praises him for destroying the pride of the Kshatriyas and for stopping the intermixture of the four varnas. He is portrayed as a champion of the Brahmanical order who defeated foreign rulers like the Sakas, Yavanas (Greeks), and Pahlavas (Parthians).
Step 3: Final Answer:
Gotami-puta Siri-Satakani is the ruler who claimed the title 'eka bamhana'.