Step 1: Understanding the Concept:
The query requires identification of the Satavahana king who adopted the title 'eka bamhana', indicating his preeminent position as a Brahmana and defender of the varna system.
Step 2: Detailed Explanation:
The assertion of being an 'eka bamhana' (the sole Brahmana) is prominently linked to Gotami-puta Siri-Satakani, a very influential monarch of the Satavahana lineage. This claim is documented in the Nashik inscription attributed to his mother, Gautami Balasri. The inscription commends him for vanquishing the arrogance of the Kshatriyas and for preventing the intermingling of the four varnas. He is depicted as a proponent of the Brahmanical hierarchy, having defeated foreign potentates such as the Sakas, Yavanas (Greeks), and Pahlavas (Parthians).
Step 3: Final Answer:
Gotami-puta Siri-Satakani is the sovereign who asserted the title 'eka bamhana'.