In a saucepan over medium, heat 1 tablespoon of olive oil, then sauté the garlic until fragrant (30 seconds to 1 minute).
Add the entire can of piquillo peppers (juices and all) to the saucepan. Stir to combine, then simmer, uncovered, over medium-low for 5 minutes, or until the juice evaporates.
Place the piquillo pepper/garlic mix into a food processor and add the smoked paprika. Process the mix until paste-like smooth and allow it to cool to room temperature.
Pour the mix into a mixing bowl and add the cream and additional tablespoon of olive oil. Stir well to combine.