Check out these vendors on the Language Resource Online website to see if they have specialized Asturian language learning courses:

Transparent I Can Speak Asturian

Transparent Asturian Now!

Transparent 101 Languages of the World Asturian

Transparent 31 Languages of the World Asturian

Auralog Asturian Beginner V5

Auralog Asturian Intermediate V5

Auralog Asturian Advanced V5

Auralog Asturian Complete V6

Eurotalk Talk Now! Asturian

Eurotalk World Talk Asturian

Eurotalk Vocabulary Builder Asturian

Topics 33 Language Instant Immersion Asturian

Topics 18 Languages Instant Immersion Asturian

Topics Asturian Instant Immersion

Topics Asturian Audio Instant Immersion

Topics Asturian Audio Advanced Instant Immersion

Topics Asturian 1.5 Instant Immersion

Topics Asturian Pro Instant Immersion

Rosetta Stone Asturian Level 1 Personal Edition

Rosetta Stone Asturian Level 2 Personal Edition