Preheat oven to 400°. Spray a mini (24-cup) muffin tin with cooking spray.
In a large pot of boiling salted water, cook pasta, stirring occasionally, until very al dente, 5 to 6 minutes. The pasta is getting cooked again in the oven, so it should be undercooked at this point.
Meanwhile, in a large skillet over medium heat, melt 2 tablespoons butter. Cook shallot and garlic, stirring occasionally, until fragrant and shallots are translucent, about 3 minutes. Whisk in flour and cook, stirring, until light brown and bubbly, about 1 minute. Reduce heat to medium-low, add cream, and cook, stirring, until it begins to thicken, about 3 minutes.
Remove skillet from heat. Add cream cheese, gouda, and cheddar and stir until melted, season with salt. Fold in lobster and pasta.
In a small skillet over medium heat, melt remaining 1 teaspoon butter. Stir in breadcrumbs until combined and fragrant. Remove from heat.
Using 2 small spoons or a small cookie scoop, divide pasta mixture among prepared cups. Sprinkle with breadcrumbs.
Bake lobster bites until golden brown and bubbly on top, 20 to 25 minutes. Top with chives; season with pepper.