Melt butter in a medium saucepan over medium heat. Cook, swirling pan occasionally, until butter begins to brown and smell nutty, about 3 minutes. Add brown sugar and cook, stirring occasionally, until sugar is starting to dissolve, about 2 minutes. Add cream, milk, bourbon, and salt; bring to a simmer. Remove from heat. Add vanilla.
Whisk egg yolks and cornstarch in a large bowl until smooth. Gradually add hot cream mixture, whisking constantly. Pour back into saucepan and cook over medium heat, stirring often, until custard bubbles occasionally and starts to thicken, 5–6 minutes.
Divide custard evenly among ramekins and chill until set, at least 3 hours. Serve with pecans and whipped cream.