Make cookies: Preheat oven to 350°. Sift flour, cocoa powder, and salt into a bowl. In another bowl with a mixer on medium speed, beat butter and granulated sugar until pale and fluffy. Reduce speed to low and add egg yolk, cream, and vanilla. Gradually beat in flour mixture.
Scoop dough into rounded 1-tsp. portions and roll into balls, then roll balls in sparkling or powdered sugar to coat. Place 2 in. apart on parchment paper-lined baking sheets. With end of a thick-handled wooden spoon, gently press an indentation into center of each cookie. Bake until cookies are just set, about 10 minutes. (The depressions tend to fill in a bit as they bake, so as soon as they're out of the oven, give them another press with the spoon if necessary.) Slide parchment with cookies onto cooling racks and let cool. If you've used powdered sugar, sift a little more onto the cookies.
Make caramel: Put granulated sugar in a large nonstick frying pan; spread evenly. Heat over medium-high heat, stirring constantly with a wooden spoon. Sugar will form clumps but eventually will melt and turn into a dark, amber-colored liquid, about 6 minutes. As soon as it's liquefied, reduce heat to medium-low. Add butter and stir until incorporated. Stirring constantly, drizzle in cream. Boil 1 minute, stirring, then remove from heat and stir in 1/4 tsp. sea salt. Scrape into a bowl and let cool completely.
Assemble cookies: Spoon about 1/4 tsp. caramel into each cookie, then sprinkle with a few grains of sea salt.
*You'll have more caramel than you need, but that's never a bad thing--it's great on ice cream. Don't be tempted to cook a half-batch of caramel, as it won't cook right and will seize up.
Make ahead: Caramel, up to 5 days, chilled (let soften at room temperature before spooning into cookies). Baked cookies, up to 1 week, chilled airtight.