Bring 6 cups of salted water to a boil in a large pot. While the water heats, prepare an ice bath by filling a large bowl with ice and cold water. Cut the broccoli heads into bite-sized 1-inch florets, then blanch them in the boiling water for exactly 1 minute—this removes the raw edge while keeping them crisp and bright green. Immediately transfer the broccoli to the ice bath to stop the cooking process, then drain and pat thoroughly dry with paper towels. Dry broccoli is crucial for preventing a watery salad, so don't skip this step.
While the broccoli cools, cook the bacon slices in a skillet over medium-high heat until crispy, about 5-7 minutes. Transfer to a paper towel-lined plate and crumble into roughly 1/2-inch pieces when cool. In a separate dry skillet or toaster oven set to 350°F, toast the slivered almonds for 3-4 minutes, stirring occasionally, until fragrant and golden—this brings out their natural oils and deepens the crunch. Set both aside to cool.
In a medium bowl, whisk together the mayonnaise, apple cider vinegar, dijon mustard, erythritol, salt, and freshly ground black pepper until smooth and well combined. The vinegar and mustard add bright acidity to balance the richness of the mayo, while the sweetener provides subtle depth without any sugar. Taste and adjust seasoning as needed—I always add a touch more salt than seems necessary because it helps marry all the flavors together.
Thinly slice the 1/4 red onion into half-moons—the thin slices add a sharp bite without overwhelming the salad. Shred or grate the cheddar cheese into small, bite-sized pieces (roughly 1/4 inch), and finely chop the fresh chives. Have all components ready before assembly, as this salad comes together quickly once you start combining.
Add the cooled blanched broccoli, dressing from Step 3, crumbled bacon from Step 2, toasted almonds from Step 2, shredded cheddar, sliced red onion, and chives to a large bowl. Toss everything together gently but thoroughly until all the broccoli florets are evenly coated with the dressing. The salad can be served immediately while the almonds are still crispy, or chilled for up to 2 hours before serving.