Put the cooked, drained, cooled white navy beans in the full-size processor bowl. Process until completely smooth, stopping to scrape the sides and beneath the rim. The paste should look pale and creamy with no bean skins or sandy flecks.

Cut the partially thawed bananas into chunks. Add them with the raw honey, raw egg yolk, and homemade vanilla. Process until glossy and uniform, with no frozen banana pieces.

Add the strawberries and pulse until the base is pale pink. Continue until the red flecks are tiny, or stop while a few very small soft strawberry pieces remain.

Transfer the slow-pouring pink base to an ice cream maker. Churn until the dasher leaves defined tracks, the mixture mounds instead of leveling immediately, and a spoonful holds a soft peak.

Serve immediately as soft serve. For a firmer result, transfer to a covered freezer container. Let fully frozen ice cream stand about 15 minutes before scooping.