Make the beets: Preheat oven to 400 degrees. Toss beets in olive oil and season liberally with salt and pepper. Wrap in aluminum foil, separating the red from yellow so the colors don’t bleed. Place foil-wrapped beets on a sheet pan and roast until easily pierced with a knife, about 45 minutes. Allow to cool slightly. Using a towel, rub skin from roasted beets. Cut into quarters and set aside.
Make the dressing: In a blender, combine garlic, oil, anchovies, herbs, and vinegar with ¼ cup of the mayonnaise. Process on high speed until smooth. Transfer to a small bowl and fold in remaining mayonnaise. Season to taste with salt and pepper.
Assemble the salad: Smear dressing across the bottom of a large serving bowl. Toss roasted beets in 2 tablespoons olive oil and season with salt and pepper, then arrange over dressing. Add smoked trout around beets. Place yellow endive and pecan pieces around plate and garnish with dollops of trout roe. Finish with salt and lemon juice.