Make the ice cream: In a large saucepan over medium heat, heat milk, cream, espresso, and sugar until just simmering. In a separate bowl, whisk egg yolks. Working fast, whisk 1 tablespoon hot milk mixture into egg yolks. Repeat this method a total of 4 times, whisking egg yolks constantly. Pour egg yolk mixture back into pan, whisking until smooth. Bring mixture to a low simmer until slightly thickened. Remove from heat and whisk in vanilla extract. Cool completely in refrigerator.
Once ice cream base is cooled, churn ice cream in an ice cream maker according to machine's instruction manual. Scrape into a container and place in freezer.
Make the caramel: In a small saucepan over medium-high heat, melt butter, sugar, and agave together. Bring to a boil, stirring occasionally until caramel is golden and thickened. Remove from heat and whisk in cream, baking soda, and salt.
While caramel is still warm, drop by the spoonful on top of churned ice cream. Use a knife to swirl caramel into the ice cream. Freeze ice cream until solid, about 2-3 hours. Enjoy!