Preheat your oven to 400°F and line a small baking sheet with parchment paper for easy cleanup. Slice the top quarter inch from each garlic head to expose the cloves, then drizzle the cut sides generously with 2 tbsp of olive oil, salt, and pepper.

Place garlic heads cut-side up on the prepared baking sheet and roast for 35 minutes until cloves are golden, caramelized, and soft enough to squeeze from their skins. The timing here is crucial—under 35 minutes and the garlic won't caramelize properly; over 40 minutes risks burning.

Remove from the oven and let cool for 5 minutes until safe to handle, then squeeze each roasted clove from its papery skin into a small bowl. Press the soft garlic with a fork until it reaches a smooth paste consistency, discarding any tough bits.

In a medium mixing bowl, beat softened cream cheese with butter and 2 tbsp heavy cream using an electric mixer until light and fluffy, approximately 2 minutes. Fold in the roasted garlic paste gently, then add sour cream, Parmesan, fresh thyme, cayenne pepper, and the remaining 1 tbsp olive oil.

Stir in balsamic vinegar and honey until just combined—these ingredients add subtle depth and balance the creamy caramelized roasted garlic dip's richness. Taste and adjust salt and pepper as needed before transferring to your serving vessel.

Drizzle the finished dip with a touch of extra olive oil and fresh thyme sprigs for visual appeal and flavor amplification. Serve immediately with high-quality crackers, toasted bread, or fresh vegetables for an elegant appetizer presentation.