The name of this warm garlicky dip comes from the term for "hot bath." In summer, serve a bowlful at room temperature, and use it to enliven vegetables at their peak. Snack on sweet, tender figs between dips.
Put milk into a shallow dish. Add anchovy fillets; soak 10 minutes. Drain on paper towels; pat dry. Coarsely chop.
Put 1/4 cup oil and the garlic into a small saucepan over low heat. Cook until garlic softens but does not brown, about 5 minutes. Add anchovies. Cook, whisking constantly, 1 minute. Add butter. Cook, whisking, until butter has melted.
Remove pan from heat. Whisk in the remaining 1/4 cup oil in a slow, steady stream until mixture thickens and comes together. If the mixture separates at any point, add 2 ice cubes, and whisk until mixture comes together; remove partially melted ice cubes.
Whisk in lemon juice, and season with salt and pepper. Serve warm or at room temperature with the vegetables.