Preheat oven to 450°F (232°C).

Remove outer leaves and core of cauliflower.

Cut cauliflower florets into 3/4" pieces.

Transfer cauliflower to a rimmed baking sheet.

Add 1/4 cup olive oil, 1 tsp. salt, and 1/2 tsp. pepper to cauliflower.

Toss to combine.

Roast, tossing once halfway through, until cauliflower is deeply charred in spots, 30-35 minutes.

Immediately grate garlic over hot cauliflower.

Toss to combine (using residual heat to soften garlic).

Set aside the roasted cauliflower.

Cook bacon in a large skillet over medium-low heat, stirring occasionally, until crisp, 8-10 minutes.

Transfer bacon and 1 Tbsp. bacon fat to a large bowl.

Add egg yolks, 1 cup Parmesan, 2 tsp. pepper, and remaining 2 Tbsp. oil to the bowl.

Whisk to combine with a fork (it will be very thick).

Cook orecchiette pasta according to package instructions; reserve 1/2 cup of cooking liquid before draining.

Add cooked pasta and 1/2 cup cooking liquid to bowl with egg yolk mixture.

Toss vigorously and continuously with a wooden spoon to create a creamy emulsified sauce that coats pasta, adding more cooking liquid as needed. Continue for at least 1 minute.

Taste and adjust seasoning, if needed.

Add roasted cauliflower and parsley and toss again to coat.

Divide pasta among bowls.

Top with more Parmesan and a few generous cranks of pepper.