Split the vanilla bean with a paring knife and scrape out seeds with the flat of the blade; reserve seeds for another use.
Combine split vanilla pod with goat’s milk, sugar, baking soda, and salt in a 5-quart stainless steel pot. Warm over medium heat, stirring occasionally with a heat-resistant spatula, until sugar dissolves and milk turns foamy and light, about 15 minutes.
Continue cooking at a gentle simmer, stirring and scraping the sides of the pot frequently if not constantly, until milk is thick, golden, and reduced to no more than a thin, super-jammy layer, about 45 minutes; stir more frequently as the cajeta thickens to prevent scorching.
Continue cooking until cajeta forms a "trail" that remains open for 1 second when a spatula is scraped across the bottom of the pot. Remove from heat. Using tongs, remove and discard vanilla pod.
Whisk in milk, cream, and vanilla into cajeta. Refrigerate until cold, at least 4 hours.
Churn in an ice cream maker until mix is well blended.