Pulse cauliflower florets in a food processor until they reach the size of small rice grains; avoid over-processing to prevent a mushy texture.
In a large, deep skillet, melt the butter with the olive oil over medium heat.
Add the minced shallots to the skillet and sauté for 3 minutes until translucent and soft.
Incorporate the minced garlic and sauté for an additional 45 seconds until aromatic.
Increase heat to medium-high and add the cauliflower rice, stirring constantly for 2 minutes to toast the grains slightly in the fat.
Deglaze the pan with chicken broth and simmer uncovered for 5 minutes, allowing the liquid to reduce by 75% while softening the cauliflower.
Reduce heat to medium-low and pour in the heavy cream. Simmer for 3-4 minutes, stirring frequently, until the cream reduces into a thick, velvety sauce.
Remove the skillet from the heat source and immediately fold in the grated Parmesan cheese until fully emulsified.
Adjust seasoning with sea salt and black pepper; garnish with chopped parsley and serve immediately to maintain the emulsion's integrity.